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Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Exercise 6(b)

Question 1.
A bag contains 5 white and 3 black marbles and a second bag contains 3 white and 4 black marbles. A bag is selected at random and a marble is drawn from it. Find the probability that it is white. Assume that either bag can be chosen with the same probability.
Solution:
A bag contains 5 white and 3 black marbles and a second bag contains 3 white and 4 black marbles. A bag is selected at random and a marble is drawn from it.
Let W₁ be the event that 1st bag is choosen and a white marble is drawn and let W₂ be the event that 2nd bag is choosen and a white marble is drawn and these two events are mutually exclusive.

Question 2.
A bag contains 5 white and 3 black balls; a second bag contains 4 white and 5 black balls; a third bag contains 3 white and 6 black balls. A bag is selected at random and a ball is drawn. Find the probability that the ball is black.
(i) Do the problem assuming that the probability of choosing each bag is same.
(ii) Do the problem assuming that the probability of choosing the first bag is twice as much as choosing the second bag, which is twice as much as choosing the third bag.
Solution:
A bag contains 5 white and 3 black balls, a 2nd bag contains 4 white and 5 black balls, a 3rd bag contains 3 white and 6 black balls. A bag is selected at random and a ball is drawn.

(i) Let B₁, B₂, B₃ be the events that 1st bag is choosen and a black ball is draw. 2nd bag is choosen and a black ball is drawn, 3rd bag is drawn and a black ball is drawn. These events are mutually exclusive.
Probability of drawing a black ball
= P(B₁) + P(B₂) + P(B₃)
= \(\frac{1}{3}\) × \(\frac{3}{8}\) + \(\frac{1}{3}\) × \(\frac{5}{9}\) + \(\frac{1}{3}\) × \(\frac{6}{9}\) = \(\frac{115}{216}\)

(ii) Let the probability of choosing 1st bag be 4x. The probability of choosing the 2nd bag is 2x and that of 3rd bag is x.
It is obvious that probability of choosing 3 bags = 1
4x + 2x + x = 1 or, 7x = 1.
x = \(\frac{1}{7}\)
Probability of drawing a black ball
= \(\frac{4}{7}\) × \(\frac{3}{8}\) + \(\frac{2}{7}\) × \(\frac{5}{9}\) + \(\frac{1}{7}\) × \(\frac{6}{9}\)
= \(\frac{108+80+48}{8 \times 9 \times 7}\) = \(\frac{236}{8 \times 9 \times 7}\) = \(\frac{59}{126}\)

Question 3.
A and B play a game by alternately throwing a pair of dice. One who throws 8 wins the game. If A starts the game, find their chances of winning.
Solution:
A and B play a game by alternately throwing a pair of dice. One who throws 8 wins the game. A starts the game.
We can obtain 8 as follows:
{(6, 2), (5, 3), (4, 4) (3, 5), (6, 2)}.
∴ |S| = 6² = 36
∴ P(B) = \(\frac{5}{36}\)
⇒ P(not 8) = 1 – \(\frac{5}{36}\) = \(\frac{31}{36}\)
Since A starts the game, A can win the following situations.
(i) A throws 8
(ii) A does not throws, B does not throw 8, A throws 8,
(iii) A does not throw 8, B does not throw 8, A does not throw 8, B does not throw 8, A throws 8, etc.

Question 4.
A, B, C play a game by throwing a pair of dice in that order. One who gets 8 wins the game. If A starts the game, find their chances of winning.
Solution:
A, B, C play a game by throwing a pair of dice in that order. One who gets 8 wins the game and A starts the game.
P(B) = \(\frac{5}{36}\), P(not 8) = \(\frac{31}{36}\)

If A starts the game, then
(i) A throws 8.
(ii) A does not throw 8, B does not throw 8, C does not throw 8, A throws 8.
(iii) A does not throw 8, B does not throw 8, C does not throw 8, A does not throw 8, B does not throw 8, C does not throw 8, A throws 8, etc.

Similarly, If B wins the game, then
(i) A does not throw 8, B throw 8.
(ii) A does not throw 8, B does not throw 8, C does not throw 8, A does not throw 8, B throws 8.
(iii) A does not throw 8, B does not throw 8, C does not throw 8, A does not throw 8, B does not throw 8, C does not throw 8, A does not throw 8, B throws 8, etc.

Question 5.
There are 6 white and 4 black balls in a bag. If four are drawn successively (and not replaced), find the probability that they are alternately of different colour.
Solution:
There are 6 white and 4 black balls in a bag. Four balls are drawn without replacement. Let W and B denotes the white and black ball. There are two mutually exclusive cases WBWB and BWBW.

Question 6.
Five boys and four girls randomly stand in a line. Find the probability that no two girls come together.
Solution:
Five boys and 4 girls randomly stand in a line such that no two girls come together.
|S| = 9!

The 4 girls can stand in 6 positions in 6P4 ways. Further 5 boys can stand in 5! ways.
Probability that they will stand in a line such that no two girls come together.
= \(\frac{5 ! \times{ }^6 P_4}{9 !}\) = \(\frac{5}{42}\)

Question 7.
If you throw a pair of dice n times, find the probability of getting at least one doublet. [When you get identical members you call it a doublet. You can get a double in six ways: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6); thus the probability of getting a doublet is \(\frac{6}{36}\) = \(\frac{1}{6}\), so that the probability of not getting a doublet in one throw is \(\frac{5}{6}\)].
Solution:
A pair of dice is thrown n times. We get
the doublet as (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6).
Probability of getting a doublet in one throw
= \(\frac{6}{36}\) = \(\frac{1}{6}\)
Probability of not getting a doublet
= 1 – \(\frac{1}{6}\) = \(\frac{5}{6}\)
If a pair of dice is thrown n-times, the probability of not getting a doublet
= \(\left(\frac{5}{6}\right)^n\)
Probability of getting atleast one doublet
= 1 – \(\left(\frac{5}{6}\right)^n\)

Question 8.
Suppose that the probability that your alarm goes off in the morning is 0.9. If the alarm goes off, the probability is 0.8 that you attend your 8 a.m. class. If the alarm does not go off, the probability that you make your 8 a.m. class is 0.5. Find the probability that you make your 8 a.m. class.
Solution:
Let A be the event that my alarm goes off and let B be the event that I make my 8 a. m. class.
Since S = a ∪ A’, B = (B ∩ A) ∪ (B ∩ A’)
Where B ∩ A and B ∩ A’ are mutually
exclusive events.
P(B) = P (B ∩ A) + P (B ∩ A’)
= P(A). P(\(\frac{B}{A}\)) + P(A’). P(\(\frac{\mathrm{B}}{\mathrm{A}^{\prime}}\))
= 0.9 × 0.8 + 0.1 × 0.5 = 0.77

Question 9.
If a fair coin is tossed 6 times, find the probability that you get just one head.
Solution:
A fair coin is tossed 6 times.
∴ |S| = 2⁶
The six mutually exclusive events are
HTTTTT, THTTTT, TTHTTT, TTTHTT, TTTTHT, TTTTTH.
Probability of getting just one head = \(\frac{6}{2^6}\)

Question 10.
Can you generalize this situation? If a fair coin is tossed six times, find the probability of getting exactly 2 heads.
Solution:
A fair coin is tossed 6 times. Let A be the event of getting exactly 2 heads.
∴ |A| = ⁶C₂ = 15
∴ P(A) = \(\frac{15}{2^6}\)
Yes we can generalize the situation, i.e., if a fair coin is tossed n-times, then probability of getting exactly 2 heads
= \(\frac{{ }^n \mathrm{C}_2}{2^n}\) = \(\frac{{ }^6 C_2}{2^6}\)

Odisha State Board BSE Odisha 7th Class English Solutions Follow-Up Lesson 8 The Fisherman and The Jinni Textbook Exercise Questions and Answers.

BSE Odisha Class 7 English Solutions Follow-Up Lesson 8 The Fisherman and The Jinni

BSE Odisha 7th Class English Follow-Up Lesson 8 The Fisherman and The Jinni Text Book Questions and Answers

Session – 1

I. Pre-Reading

• Socialisation (ସାମାଜିକୀକରଣ)
• The teacher prepares a good pre-reading activity on his / her own as done for the main lesson

II. While-Reading

• Read the following text silently and answer the questions that follow.
(ନିମ୍ନ ବିଷୟଟିକୁ ନୀରବରେ ପଢ଼ ଏବଂ ନିମ୍ନ ପ୍ରଶ୍ନଗୁଡିକର ଉତ୍ତର ଦିଅ ।)
There lived a poor fisherman with his wife and children in a hut near the sea. Everyday he used to go to the sea and catch fish. ’
One day, as usual, he went to the sea. He threw his net into the sea, and when he pulled it out, he felt it very heavy. But there was no fish in it. He saw a log of wood in the net. He felt sad. He threw the net for the second time. This time he got a few shells and big stones. When he tried it for the third time, he found it heavier. This time too he did not see any fish in it but a big brass jar with a lid.
Taking the jar out of the net, he opened it. A lot of smoke came out of it. Suddenly a jinni appeared in the smoke. On seeing the jinni, he screamed. “I’ll kill you now” shouted the jinni.
“Why ?” asked the fisherman and said, “I haven’t done you any harm. Please don’t kill me.”
“I was in the jar. I was not free. Now I am free. I will kill you and eat you up” said the jinni. The fisherman was afraid of the jinni. He did not know what to do. Suddenly he got a clever idea and said, “Alright, you can kill me but I don’t believe what you say. You are very big. How could you come out of this jar ?”
The jinni got angry. “How dare you say I cannot come out of this jar ? I can take any form. I can take the form of an elephant or become even a small ant,” said the jinni.
“Is it so ? Can you become an ant ?” said the fisherman cleverly.
“Surely,” said the jinni and immediately took the form of an ant and got into the jar again. The fisherman immediately shut the jar tight and said with a grin, “Now I believe your story, my friend, you cannot come out any more and kill me ?” Then he threw the jar into the sea and returned home happily.

ଓଡ଼ିଆ ଅନୁବାଦ :
ସମୁଦ୍ର ପାଖରେ ଗୋଟିଏ କୁଡ଼ିଆ ଘରେ ଜଣେ ବିଚାରା କେଉଟ ତା’ର ସ୍ତ୍ରୀ ଏବଂ ପିଲାମାନଙ୍କୁ ନେଇ ବାସ କରୁଥିଲା । ପ୍ରତ୍ୟେକ ଦିନ ସେ ସମୁଦ୍ରକୁ ଯାଇ ମାଛ ଧରିବାରେ ଅଭ୍ୟସ୍ତ ଥିଲା ।
ଦିନେ ସ୍ୱାଭାବିକ ଭାବରେ ସେ ସମୁଦ୍ରକୁ ଗଲା । ସେ ତା’ ଜାଲକୁ ସମୁଦ୍ର ଭିତରକୁ ଫିଙ୍ଗିଲା ଏବଂ ଯେତେବେଳେ ସେ ତାହାକୁ ବାହାରକୁ ଟାଣିଲା ତାକୁ ବହୁତ ଓଜନିଆ ଜଣାଗଲା । କିନ୍ତୁ ତା’ ଭିତରେ ମାଛ ନଥିଲା । ସେ ଖଣ୍ଡେ କାଠଗଣ୍ଡି ଜାଲ ଭିତରୁ ପାଇଲା । ସେ ଦୁଃଖ୍ ହେଲା । ସେ ଜାଲକୁ ଦ୍ଵିତୀୟବାର (ସମୁଦ୍ର ଭିତରକୁ) ଫିଙ୍ଗିଲା ।
ତାହା ଅଧ୍ଵକ ଓଜନିଆ ଲାଗିଲା । ଏଥର ମଧ୍ୟ ସେ ସେଥ‌ିରେ କୌଣସି ମାଛ ଦେଖିବାକୁ ପାଇଲା ନାହିଁ; କିନ୍ତୁ ଗୋଟେ ବଡ଼ ଠିପି ଲାଗିଥିବା ପିତ୍ତଳ ଜାର୍ ପାଇଲା ।
ଜାର୍‌ଟିକୁ ଜାଲରୁ ପଦାକୁ ଆଣି ସେ ତାହାକୁ ଖୋଲିଲା । ତା’ ମଧ୍ୟରୁ ବହୁତ ଧୂଆଁ ବାହାରିଲା । ହଠାତ୍ ସେଥ୍ ମଧ୍ୟରୁ ଗୋଟେ ଭୂତ ଆବିର୍ଭାବ ହେଲା । ଭୂତକୁ ଦେଖୁ ସେ ଚିହିଁକି |ଚିତ୍କାର କରି ଉଠିଲା । ଭୂତ ତାକୁ ଚିତ୍କାର କରି କହିଲା, ‘ବର୍ତ୍ତମାନ ମୁଁ ତୋତେ ମାରିଦେବି ।’’
“‘କାହିଁକି ?’’ କେଉଟ ପଚାରିଲା ଏବଂ କହିଲା, ‘ମୁଁ ତୁମର କିଛି କ୍ଷତି କରିନାହିଁ । ଦୟାକରି ମୋତେ ମାରନାହିଁ ।’’
ଭୂତ କହିଲା, ‘‘ମୁଁ ଜାର୍ ଭିତରେ ଥୁଲି । ମୁଁ ମୁକ୍ତ ନଥୁଲି । ବର୍ତ୍ତମାନ ମୁଁ ମୁକ୍ତ । ମୁଁ ତୁମକୁ ମାରିଦେବି ଏବଂ ଖାଇବି ।’’ କେଉଟ ଭୂତକୁ ଭୟ କରିଗଲା । ସେ କ’ଣ କରିବାକୁ ହେବ ଜାଣିପାରିଲା ନାହିଁ । ହଠାତ୍ ତା’ ମୁଣ୍ଡରେ ଗୋଟେ ଚାଲାକି ବୁଦ୍ଧି ଜୁଟିଲା ଏବଂ ସେ କହିଲା, ‘ଠିକ୍ ଅଛି, ତୁମେ ମୋତେ ମାରିଦେଇ ପାରିବ; କିନ୍ତୁ ତୁମେ ଯାହା କହୁଛ ମୁଁ ବିଶ୍ବାସ କରିପାରୁନି । ତୁମେ ତ ବହୁତ ବଡ଼ । ତୁମେ କିପରି ଏହି (ଛୋଟ) ଜାରରୁ ଆସିପାରିଲ ?’’
ଭୂତ ରାଗିଗଲା । ସେ କହିଲା, ‘ତୁମର କିପରି କହିବାକୁ ସାହସ ହେଲା ଯେ ମୁଁ ଏହି (ଛୋଟ) ଜାର୍ ଭିତରୁ ବାହାରକୁ ଆସିପାରି ନଥା’ନ୍ତି। ମୁଁ ଯେକୌଣସି ଆକାର ପ୍ରକାରର ହୋଇପାରେ । ମୁଁ ଗୋଟେ ହାତୀ ଆକୃତିର ହୋଇପାରେ ଏବଂ ଏପରିକି ଗୋଟେ ଛୋଟ ପିମ୍ପୁଡ଼ି ଆକାରର ମଧ୍ୟ ହୋଇପାରେ ।’’
କେଉଟ ବଡ଼ ଚାଲାକିରେ କହିଲା, ‘ଏହା କ’ଣ ତାହାହେଲେ ସେଇଆ ? ତୁମେ ଗୋଟେ ପିମ୍ପୁଡ଼ି ବି ହୋଇପାରିବ ?’’
ଭୂତ କହିଲା, ‘ନିଶ୍ଚୟ’ ଏବଂ ତତ୍‌କ୍ଷଣାତ୍ ଗୋଟିଏ ପିମ୍ପୁଡ଼ିର ଆକାର ଧାରଣ କରି ଜାର୍ ମଧ୍ୟକୁ ପୁନର୍ବାର ପ୍ରବେଶ କଲା । କେଉଟ ତତ୍‌କ୍ଷଣାତ୍ ଜାର ଠିପିଟିକୁ ଜୋର୍‌ରେ ବନ୍ଦ କରିଦେଲା ଏବଂ ଅଳ୍ପ ହସିକରି କହିଲା, ‘ବର୍ତ୍ତମାନ ମୁଁ ତୁମ କାହାଣୀକୁ ବିଶ୍ୱାସ କଲି, ହେ ବନ୍ଧୁ । ତୁମେ ଆଉ କେବେ ପଦାକୁ ଆସିପାରିବ ନାହିଁ କି ମୋତେ ମାରି ପାରିବ ନାହିଁ ।’’ ତା’ପରେ ସେ ଜାର୍‌ଟିକୁ ସମୁଦ୍ର ମଧକୁ ଫୋପାଡ଼ି ଦେଲା ଏବଂ ମନଖୁସିରେ ଘରକୁ ଫେରିଲା ।

Notes And Glossary:
fisherman (ଫିସର ମ୍ୟାନ୍ ) – କେଉଟ
hut (ହଟ୍) – କୁଡ଼ିଆଘର
sea – ସମୁଦ୍ର
used to (ଇଉଡ଼ ଟୁ) – ବରାବର । ନିୟମିତ ଭାବରେ
catch (କ୍ୟାଚ୍) – ଧରିବା
as usual (ଆଜ୍ ୟୁଜୁଆଲ୍) – ସବୁଦିନ ପରି
threw – ପକାଇଲା | ଫିଙ୍ଗିଲା
net (ନେଟ୍) – ଜାଲ
pulled (ପୁଲ୍‌) – ଟାଣିଲା | ଓଟାରିଲା
felt (ଫେଲ୍‌ଟ) – ଅନୁଭବ କଲା
heavy – ମୋଟା
log (ଲଗ) – କାଠଗଣ୍ଠି
wood (ଉଡ୍) – କାଠ
shells (ସେଲ୍‌ସ୍) – ଶାମୁକାସବୁ
stones (ଷ୍ଟୋନ୍‌ସ) – ଗୋଡ଼ିପଥର ସବୁ
tried (ଟ୍ରାଏଡ୍) – ଚେଷ୍ଟା କଲା
found (ଫାଉଣ୍ଡ୍) – ଦେଖୁବାକୁ ପାଇଲା
brass (ବ୍ରାସ୍ ) – ପିତ୍ତଳ
jar – ପାତ୍ର
lid – ଠିପି | ଢାଙ୍କୁ ଣି
smoke (ସ୍ପୋକ୍) – ଧୁଆଁ
suddenly (ସଡ଼ଲି) – ହଠାତ୍
jini – ଜିନି
appeared (ଆପିଅର୍‌ଡ଼) – ଉପସ୍ଥିତ ହେଲା
screamed (ସ୍କ୍ରିମ୍‌ଡ୍) – ଚିତ୍କାର କଲା
harm (ହାର୍ମ) – କ୍ଷତି
free – ମୁକ୍ତ
afraid (ଆଫ୍ରେଡ୍‌) – ଭୟଭୀତ
clever (କ୍ଲେଭର) – ଚତୁର
idea (ଆଇଡ଼ିଆ ) – ବୁଦ୍ଧି / ଯୋଜନା
believe (ବିଲିଭ୍ ) – ବିଶ୍ଵାସ କରିବା
angry (ଆଙ୍ଗ୍ରି) – ରାଗିଯିବା
dare (ଡେୟାର) – ସାହସ କରିବା-
form – ରୂପ / ଆକାର
elephant (ଏଲିଫାଣ୍ଟ୍‌) – ହାତୀ
ant (ଆଣୁ) – ପିମ୍ପୁଡ଼ି
small (ସ୍ମଲ୍) – ଛୋଟ
surely (ସିଓର୍‌ଲି) – ନିଶ୍ଚିତ ଭାବରେ
immediately (ଇମିଡ଼ିଏଟ୍‌ଲି) – ଖୁବ୍ ଶୀଘ୍ର
shut (ସଟ୍) – ବନ୍ଦ କରିଦେବା
tight (ଟାଇଟ୍) – କଠିନ ଭାବରେ
grin (ଗ୍ରିନ୍) – ଚିକ୍କଣ କରିବା
any more (ଏନି ମୋର) – ଆଉ କେବେ
kill – ହତ୍ୟା କରିବା
returned (ରିଟର୍ଣ୍ଣଡ୍) – ଫେରି ଆସିଲା
home (ହୋମ୍) – ଘରକୁ
happily (ହାପିଲି) – ଖୁସି | ଆନନ୍ଦରେ

Comprehension Questions

Question 1.
Who are there in this story ?
(ଏହି ଗପଟିରେ କେଉଁମାନେ ଅଛନ୍ତି ?)
Answer:
A fisherman and a jinny are there in the story.

Question 2.
Where did the fisherman live ?
(କେଉଟ କେଉଁଠାରେ ବାସ କରୁଥିଲା ?)
Answer:
The fisherman lived in a hut near the sea with his wife and children.

Question 3.
What did the fisherman do at the sea everyday ?
(କେଉଟ ପ୍ରତିଦିନ ସମୁଦ୍ରରେ କ’ଣ କରୁଥିଲା ?)
Answer:
The fisherman went to the sea everyday and caught fish.

Question 4.
What did the fisherman see in his net when he pulled it out third time ?
(କେଉଟ ତା’ ଜାଲରେ କ’ଣ ଦେଖିଲା ଯେତେବେଳେ ତୃତୀୟବାର ସେ ତାହା (ଜାଲ)କୁ ପଦାକୁ ଟାଣି ଆଣିଲା ?)
Answer:
When the fisherman pulled his net out third time, he saw a big brass jar with a lid in it.

Question 5.
What did the fisherman do with the brass jar ?
(କେଉଟ ପିତ୍ତଳ ଜାର୍‌ଟିକୁ କ’ଣ କଲା ?)
Answer:
The fisherman took the brass jar out of the net and opened it.

Question 6.
What happened when he opened the lid of the brass jar ?
(ସେ ପିତ୍ତଳ ଜାର୍‌ଟିର ଘୋଡ଼ଣି ଖୋଲିଦେଲା ପରେ କ’ଣ ହେଲା ? )
Answer:
When he opened the lid of the brass jar, a lot of smoke came out of it. Suddenly a jinni appeared in the smoke.

Question 7.
What did the jinni say to the fisherman when he came out of the jar ?
(ଭୂତଟି ଜାର୍ ମଧ୍ୟରୁ ବାହାରକୁ ଆସିଲା ପରେ କେଉଟକୁ କ’ଣ କହିଲା ?)
Answer:
When the jinni came out of the jar, he said to the fisherman to kill him.

Question 8.
What idea did the fisherman get to get rid of the jinni ?
(କେଉଟ ଭୂତ କବଳରୁ ରକ୍ଷା ପାଇବାକୁ କି ଉପାୟ ପାଞ୍ଚିଲା ?)
Answer:
Suddenly the fisherman got a clever idea. He planned to get the jinni into the brass jar again by his cleverness.

Question 9.
What form did the jinni take to get into the jar again ?
(ପୁନର୍ବାର ଜାର୍ ମଧ୍ୟରେ ପ୍ରବେଶ କରିବାପାଇଁ ଭୂତ କି ରୂପ ଧାରଣ କଲା ?)
Answer:
Jinni took the form of a small ant to get into the jar again.

Question 10.
What did the fisherman do when the jinni got into the jar ?
(ଭୂତ ଜାର୍ ମଧ୍ୟକୁ ପ୍ରବେଶ କଲାମାତ୍ରେ କେଉଟ କ’ଣ କଲା ?)
Answer:
When the jinni got into the jar, the fisherman suddenly shut the jar tight and threw it into the sea.

Question 11.
What did he do to the jar and the jinni in the end ?
(ସେ ସର୍ବଶେଷରେ ଜାର୍ ଏବଂ ଭୂତକୁ କ’ଣ କଲା ?)
Answer:
In the end, he threw the jar containing jinni into the sea.

Session – 2

III. Post-Reading

1. Visual Memory Development Technique (VMDT) :
(ଦୃଶ୍ୟ ସ୍ମୃତି ବିକାଶ କୌଶଳ)
The teacher prepares this activity on his / her own.

2. Comprehension Activities :
Given below are some sentences from the story. They are not in order. Arrange them in right order. Write serial numbers in brackets. (Question with Answer)

(i) Then he threw the jar into the sea. (8)
(ii) This time he got some stones in the sea. (4)
(iii) There appeared a jinni in the smoke. (5)
(iv) Once there lived a fisherman in a hut with his family near the sea. (1)
(v) Soon the jinni became an ant and got into the jar. (7)
(vi) One day when he pulled out the net, he saw a log of wood in it. (2)
(vii) He became sad and threw the net into the sea for the second time. (3)
(viii) The jinni said, “I’ll kill you.” (6)
Note to the teachers : [Frame other post-reading activities on your own]

Word Note:
Jinni (ଜିନ୍ନି |) – ghost (ଭୂତ)
beast – animal (ପଶୁ)
clever – wise (ଚତୁର, ଚାଲାକ)
distrust (ଡିସ୍‌ଟ୍ରଷ୍ଟ) – do not believe (ଅବିଶ୍ବାସ କରିବା)
disappointed (ଡିସାପଏଣ୍ଟେଡ୍) – became unhappy (ଦୁଃଖୀ ହେଲେ)
expect (ଏକ୍ସପେକୁ) – something you hope to get ( ଆଶା କରିବା )
form (ଫର୍ମ) – shape, body (ଆକାର)
gratitude – feeling of thankfulness (କୃତଜ୍ଞତା)
grin (ଗ୍ରିନ୍) – smile broadly (ହସ)
idiot (ଇଡ଼ିଅଟ୍) – one who fails to understand simple things (ନିର୍ବୋଧ, ବୋକା)
interrupting (ଇଣ୍ଟେରପ୍‌ଟିଙ୍ଗ୍) – breaking the continuity (ମଝିରେ ବାଧା ଦେଇ)
judgement (ଜଜ୍ମେଣୁ) – decision (ନିଷ୍ପଭି, ମତାମତ, ବିଚାର)
mixed up (ମିକ୍ସଡ୍ ଅପ୍) – became very confusing ( ହୋଇଯିବା, ବୁଝା ନ ପଡ଼ିବା)
patience (ପେସେନ୍ସ) – ability to wait for something for long time or to deal with something without getting angry ( ଧୈର୍ଯ୍ୟ, ସହନଶୀଳଭାବ)
pity (ପିଟି) – sadness that you feel when someone else is hurt or in trouble (ଦୟା, ଅନୁକମ୍ପା)
rage (ରେଜ୍) – anger (କ୍ରୋଧ)
repay (ରିପେ) – to give back something (ଫେରାଇବା, ପ୍ରତିଦାନ)
screamed (ସ୍କ୍ରିମ୍‌ଡ୍) – gave a cry with fear (ଚିତ୍କାର କରିବା)
seize (ସିଜ୍) – to take hold of forcibly (ହଠାତ୍ ଜବରଦସ୍ତ ଧରି)
shells (ସେଲ୍‌ସ୍) – water creatures like snail, oyster etc. having harder outer covering
shelter – place to live ( ଆଶ୍ରୟସ୍ଥଳ)
slave – servant (କ୍ରୀତଦାସ)
starve – to have no food (ଅନାହରରେ ରହିବା)
tale – story
trap (ଟ୍ରାପ୍) – an instrument for catching animals
tremble (ଟ୍ରିମ୍ବଲ୍) – shake in fear
trust (ଟ୍ରଷ୍ଟ୍) – faith (ବିଶ୍ୱାସ )
ungrateful (ଅଗ୍ରେଟ୍‌ଫୁଲ୍) – (a negative quality) not being thankful to a person who does some favour to you
witness (ଉଇଟ୍‌ନେସ୍) – a person who sees something happen

BSE Odisha 7th Class English Solutions Follow-Up Lesson 8 The Fisherman and The Jinni Important Questions and Answers

(A) Choose the right answer from the options.

Question 1.
When the fisherman pulled out the net first time he found .
(a) fish
(b) bottles
(c) a log of wood
(d) a copper bottle.
Answer:
(c) a log of wood

Question 2.
When the fisherman pulled out the net third time he found in it.
(a) log of wood
(b) some shells
(c) big stones
(d) a big brass jar
Answer:
(d) a big brass jar

Question 3.
When the fisherman opened the brass jar he found .
(a) a piece of gold
(b) a bag of sand
(c) a lot of smoke coming out
(d) some stones
Answer:
(c) a lot of smoke coming out

Question 4.
When the Jinni appeared, he wanted.
(a) to his gratitude
(b) to kill the fisherman
(c) to help the fisherman in future
(d) to go away
Answer:
(b) to kill the fisherman

Question 5.
The Jinni entered into the brass jar taking the form of
(a) an ant
(b) smoke
(c) water
(d) a fly
Answer:
(a) an ant

(B) Answer the following questions.
Question 1.
What did the fisherman get when he pulled out his net second time ?
Answer:
The fisherman got a few shells and big stones when he pulled out his net second time.

Question 2.
How did the fisherman let the jinni got into the jar ?
Answer:
The fisherman knew that the Jinni would kill him. Then he pretended to be foolish and asked the jinni that he was so big and he did not believe that he was inside the jar. So he wanted to see it. The Jinni could not understand his trick. He took the form of an ant and entered the jar. The fisherman very soon shut the jar tightly.

Question 3.
Who was clever- the fisherman or the jinni ?
Answer:
The fisherman was clever enough to put the Jinni inside the jar.

(B) Re-arrange the jumbled words to make meaningful sentences.

1. Brahman / O, / let / out / me / cage / of / his / pious
2. and / let / out / I / me / serve /will / you / for/as / slave/a / whole/life
3. by / who / don’t / shade /17 and / give / shelter/everyone / to / who / passes /?
4. services / for / past / the / reward/master / does / me / my /?
5. you / the / is / too / trap / small / hold / to
Answer:
1. Let me out of this cage, O, pious Brahman!
2. Let me out, and I will serve you as a slave for my whole life.
3. Don’t I give shade and shelter to everyone who passes by?
4. Does my master reward me for past services?
5. the trap is too small to hold you.

(C) Find whether True or False.
1. Let me out of the cage, O, pious jackal!
2. You must be a fool to expect gratitude from a hungry beast.
3. Does not my master reward me for past services?
4. The jackal was caught in a trap.
5. The tiger lost patience and at once jumped into the trap.
6. There lived a rich man with his wife and children.
7. every day he used to go to the river and catch fish.
8. Suddenly a jinni appeared in the smoke.
Answer:
(1) False
(2) True
(3) False
(4) False
(5) True
(6) False
(7) False
(8) True

Odisha State Board BSE Odisha 7th Class English Solutions Tail-Piece Lesson Branding Babies by Hot Iron Rods-A Bad Practice

BSE Odisha Class 7 English Solutions Tail-Piece Lesson Branding Babies by Hot Iron Rods-A Bad Practice

BSE Odisha 7th Class English Tail-Piece Lesson Branding Babies by Hot Iron Rods-A Bad Practice

I. Pre-Reading (ପୂର୍ବ ପ୍ରସ୍ତୁତି)
You have already read the lesson “Birsa Munda”. Birsa Munda fought against superstition in the society. Read the following text to know about some other bad practices in our society. We will also know what we have to do.
(‘ବିର୍ସା ମୁଣ୍ଡା’ ବିଷୟ ତୁମେ ପଢ଼ିସାରିଛ । ବିର୍ସା ମୁଣ୍ଡା ସମାଜର କୁସଂସ୍କାର ବିରୋଧରେ ଲଢ଼ୁଥିଲେ । ଆମ ସମାଜରେ ଅନ୍ୟାନ୍ୟ ମନ୍ଦ ପ୍ରଥା ବିଷୟରେ ଜାଣିବାକୁ ନିମ୍ନ ପାଠ୍ୟବିଷୟକୁ ପଢ଼ । ଆମକୁ କ’ଣ କରିବାକୁ ହେବ ତାହା ମଧ୍ୟ ଆମେ ଜାଣିବା ।)

→ Look at the following newspaper headings and pictures.
(ଖବରକାଗଜର ନିମ୍ନ ଶିରୋନାମାକୁ ଏବଂ ଛବିକୁ ଦେଖ ।)

→”Branding by Hot Iron Rods Kills Five Babies in Nawarangpur.”
(‘‘ଶିଶୁମାନଙ୍କୁ ତତଲା ଲୁହାଛଡ଼ରେ ଚେଙ୍କ ନବରଙ୍ଗପୁରର ପାଞ୍ଚଜଣ ଶିଶୁଙ୍କ ଜୀବନ ନେଲା ।’’)

→”Seven Babies Die in Two Months Due to Branding.”
(‘‘ଚେଙ୍କ ଯୋଗୁଁ ଦୁଇ ମାସରେ ସାତଜଣ ଶିଶୁଙ୍କ ପ୍ରାଣ ଗଲା ।’’)

→Do you think these are good practices?
(ତୁମେ କ’ଣ ଭାବୁଛ ଏଗୁଡ଼ିକ ଭଲ ପ୍ରଥା ?)

→Do you have a role to play against such practices ?(ଏହି ପ୍ରଥାଗୁଡ଼ିକ ବିରୋଧରେ ତୁମର କିଛି ଭୂମିକା ଗ୍ରହଣ କରିବାର ଅଛି କି ?)Read the following text to know what you can do to stop such bad things from the society. (ସମାଜରୁ ଏଭଳି ଖରାପ ପ୍ରଥାଗୁଡ଼ିକୁ ବନ୍ଦ କରିବା ନିମିତ୍ତ ତୁମେ କ’ଣ କରିପାରିବ ତାହା ଜାଣିବା ପାଇଁ ନିମ୍ନ ପାଠ୍ୟ ବିଷୟକୁ ପଢ଼ ।)

II. While Reading (ପଠନକାଳୀନ)
Text(ପାଠ୍ୟବସ୍ତୁ)

• SGP-1 (Sense Group Paragraph-1)
• Read the following text silently and answer the questions that follow.
  (ନିମ୍ନ ପାଠ୍ୟ ବିଷୟକୁ ନୀରବରେ ପାଠ କର ଏବଂ ନିମ୍ନସ୍ଥ ପ୍ରଶ୍ନଗୁଡ଼ିକର ଉତ୍ତର ଦିଅ ।)

Every month two or three babies die due to branding in our state. When a baby has a fever or diarrhea or any other diseases, the illiterate parents and grandparents call the village quack, the disari. The quack, the village doctor puts hot iron rods on the stomach of the babies as a cure. Instead of getting cured, the babies die. But these blind practices continue. What can we do to check such blind practices? You are studying in schools. You know if we suffer from diseases, we should go to a qualified doctor, not to an illiterate disari or a village quack. As you are educated, you have a role to play in this regard. Tell the people not to go to a disari or a village quack. Ask them to go to a hospital for treatment. Talk to your classmates, form a group to fight against the bad and blind practices of branding in and around your village and locality.

ଓଡ଼ିଆ ଅନୁବାଦ :
ଆମ ରାଜ୍ୟରେ ପ୍ରତ୍ୟେକ ମାସରେ ଦୁଇରୁ ତିନିଜଣ ଶିଶୁ ଚେଙ୍କଦ୍ଵାରା ପ୍ରାଣ ହରାଉଛନ୍ତି । ଗୋଟିଏ ଶିଶୁକୁ କୌଣସି ଜ୍ଵର, ଝାଡ଼ାରୋଗ କିମ୍ବା ଅନ୍ୟ କିଛି ରୋଗ ହେଲେ, ଶିଶୁର ନିରକ୍ଷର ପିତାମାତା କିମ୍ବା ଜେଜେ ଓ ଜେଜେମା’ ଗ୍ରାମ ବୈଦ୍ୟ (ଦିସାରୀ) ଙ୍କୁ ଡକାନ୍ତି । ବୈଦ୍ୟ ବା ଗ୍ରାମ ଡାକ୍ତର ଆରୋଗ୍ୟ ନିମିତ୍ତ ଶିଶୁର ପାକସ୍ଥଳୀରେ । ଏପ୍ରକାର ଅନ୍ଧ ପ୍ରଥା ଚାଲୁ ରହିଛି । ଏ ପ୍ରକାର ଅନ୍ଧ ପ୍ରଥାକୁ ବନ୍ଦ କରିବାକୁ ଆମେ ସବୁ କ’ଣ କରିପାରିବା ? ତୁମେମାନେ ବିଦ୍ୟାଳୟରେ ପାଠ ପଢୁଛ । ତୁମେ ତ ଜାଣ, ଆମକୁ ଯଦି ରୋଗ ହୁଏ, ତେବେ ଆମେ ଜଣେ ଯୋଗ୍ୟ ଡାକ୍ତରଙ୍କ ପାଖକୁ ଯିବା ଉଚିତ ହେବ । ଜଣେ ଅଶିକ୍ଷିତ ଦିସାରୀ ବା ଗ୍ରାମ୍ୟ ବୈଦ୍ୟ ପାଖକୁ ନୁହେଁ । ଯେଣୁ ତୁମେ ଶିକ୍ଷିତ ତୁମର ମଧ୍ୟ ଏଥିପାଇଁ କିଛି ଭୂମିକା ଅଛି । ଲୋକମାନଙ୍କୁ କୁହ – ବୁଝାଅ ଦିସାରୀ ବା ଗ୍ରାମ୍ୟ ବୈଦ୍ୟ ପାଖକୁ ଯିବା ଦରକାର ନାହିଁ । ବୁଝାଇ ଦିଅ (ରୋଗ ହେଲେ) ଡାକ୍ତରଖାନାକୁ ଚିକିତ୍ସା ନିମିତ୍ତ ଯାଆନ୍ତୁ । ଶ୍ରେଣୀର ସାଥୀମାନଙ୍କ ସହିତ କଥା ହୁଅ, ଦଳବାନ୍ଧି ତୁମ ଗ୍ରାମ ବା ଅଞ୍ଚଳ ଅଥବା ଆଖପାଖ ଗ୍ରାମ ଓ ଅଞ୍ଚଳରେ ଏ ପ୍ରକାର ଖରାପ ଅନ୍ଧପ୍ରଥା ବିରୋଧରେ ସଂଗ୍ରାମ କର ।

Notes And Glossary: (ଶବ୍ଦାର୍ଥ) :
die (ଡାଏ) – ମର
due to (ଡିଭ ଟୁ) – ଯୋଗୁ
branding (ବ୍ରାଣ୍ଡିଙ୍ଗ୍‌) – ଚେଙ୍କ
state (ଷ୍ଟେଟ୍) – ରାଜ୍ୟ
fever (ଫିଭର୍) – ଜ୍ୱର
diarrhea (ଡାଇରିଆ) – ହଇଜା
diseases (ଡିଜିଜେସ୍) – ରୋଗ ସବୁ
illiterate (ଇଲିଟ୍‌ରେଟ୍) – ନିରକ୍ଷର
quack – କୋଳାହଳ କରିବା
stomach (ଷ୍ଟୋମାକ୍) – ପେଟ
cure – ଆରୋଗ୍ୟ
instead of (ଇଡ୍‌ ଅଫ୍) – ପରିବର୍ତ୍ତେ
blind practice (ବ୍ଲାଇଣ୍ଡ୍ ପ୍ରାକ୍‌ଟିସ୍) – ଅନ୍ଧ ଅଭ୍ୟାସ
check (ଚେକ୍) – ଯାଞ୍ଚ କରନ୍ତୁ
suffer (ସଫର) – ଯନ୍ତ୍ରଣା ଭୋଗ
qualified (କ୍ଵାଲିଫାଇଡୁ) – ପ୍ରଶିକ୍ଷିତ
educated (ଏଜୁକେଟେଡ୍) – ଶିକ୍ଷିତ
role (ରୋଲ୍) – ଭୂମିକା
play – ଗ୍ରହଣ କରିବା
regard – ସମ୍ମାନ କରିବା
treatment (ଟ୍ରିଟ୍‌ମେଣ୍ଟ୍‌) – ଚିକିତ୍ସା
form – ଫର୍ମ
locality (ଲୋକାଲିଟି) – ଅଞ୍ଚଳ

Comprehension Questions (ବୋଧପରିମାପକ ପ୍ରଶ୍ନବଳୀ) :
Question 1.
What is the topic about?
(ବିଷୟଟି କେଉଁ ବିଷୟରେ ଉଦ୍ଦିଷ୍ଟ ?)
Answer:
The topic is about the blind belief or bad practice of branding babies by hot iron rods for cure in and around our village and locality.

Question 2.
What happens to two to three babies in our state every month?
(ଆମ ରାଜ୍ୟରେ ପ୍ରତ୍ୟେକ ମାସରେ ଦୁଇ ତିନିଜଣ ଶିଶୁଙ୍କର କ’ଣ ହୁଏ | ଘଟେ ?)
Answer:
In our state, every month two or three babies die due to branding.

Question 3.
When do illiterate people or grandparents call a village quack?
(କେତେବେଳେ ଅଶିକ୍ଷିତ ଗ୍ରାମବାସୀମାନେ.କିମ୍ବା ଜେଜେ ବାପା ଓ ଜେଜେମା’ମାନେ ଗ୍ରାମ ବୈଦ୍ୟଙ୍କୁ ଡକାନ୍ତି ?)
Answer:
The illiterate people and grandparents call a village quack when a baby has fever or any diseases.

Question 4.
Do you think it is a good practice?
(ତୁମେ କ’ଣ ଭାବୁଛ ଏହା ଏକ ଠିକ୍ | ଭଲ ପ୍ରଥା ?)
Answer:
No, we think branding babies is not a good practice.

Question 5.
What does the village quack do?
(ଗ୍ରାମ ବୈଦ୍ୟ କ’ଣ କରେ ?)
Answer:
The village quack puts hot iron rods on the stomach of the babies as a cure.

Question 6.
Why does he put the hot iron rods on the stomach of the babies?
(ସେ ଶିଶୁମାନଙ୍କ ପାକସ୍ଥଳୀରେ/ପେଟରେ କାହିଁକି ତତଲା ରଡ଼ର ଚେଙ୍କ ଦେଇଥା’ନ୍ତି ? )
Answer:
He puts hot iron rods on the stomach of the babies to cure them from the disease.

Question 7.
Do the babies get well? What happens to them?
(ଶିଶୁମାନେ କ’ଣ ଆରୋଗ୍ୟ ଲାଭ କରନ୍ତି ? ସେମାନଙ୍କର କ’ଣ ହୁଏ ?)
Answer:
No, the babies do not get well. Instead of getting well they die.

Question 8.
Where should we go to if we suffer from a -disease?
(ଆମକୁ କୌଣସି ରୋଗ ହେଲେ ଆମେ କେଉଁଠାକୁ ଯିବା ଉଚିତ ?)
Answer:
If we suffer from a disease we should go to a qualified doctor.

Question 9.
Who shouldn’t we go to?
(ଆମେ କାହା ପାଖକୁ ନଯିବା ଉଚିତ ?)
Answer:
We should not go to a village quack, the disari.

Question 10.
What have you got to do? Why?
(ତୁମର କ’ଣ କରିବାକୁ ଅଛି ? କାହିଁକି ?)
Answer:
We have to work to check such blind practices because these practices do harm to our society.

Question 11.
What should you tell the people?
(ତୁମେ ଲୋକଙ୍କୁ କ’ଣ କହିବା | ବୁଝାଇବା ଉଚିତ ?)
Answer:
We should tell the people to go to a qualified doctor not to a village quack or disari, if anybody suffers from illness.

Question 12.
What do you think is a better place to go – a village quack or a doctor ?
କେଉଁଠିକୁ ଯିବା ଭଲ ହେବ – ଗୁଣିଆ ନା ଚିକିତ୍ସକ (ଡାକ୍ତର) ପାଖକୁ ?)
Answer:
We think it is better to go to a qualified doctor not to an illiterate village quack or disari.

Question 13.
What should you do?
(ତୁମେମାନେ କ’ଣ କରିବା ଉଚିତ ?)
Answer:
We should talk to our classmates and form a group to fight against the blind or bad practice of branding babies in and around our village and locality.

Notes And Glossary: (ଶବ୍ଦାର୍ଥ) :
battle (ବ୍ୟାଟଲ୍) – fight (ସଂଘର୍ଷ, ଯୁଦ୍ଧ)
beat – no one can do better in arrow shooting, defeat (ହରାଇ ପାରିବା)
beaten (ବିଟେନ୍) – punished with heavy thrashing (ମାଡ଼ ଖାଇଥିଲେ )
branding (ବ୍ରାଣ୍ଡିଙ୍ଗ୍‌) – giving marks with hot iron
captured (କ୍ୟାପ୍‌ଚର୍‌ଡ୍) – caught (him) (ଧରି ନେଇଥିଲେ)
cowboy (କାଓବଏ) – someone who looks after cows (ଗାଈ ଜଗୁଆଳ)
defeated (ଡିଫିଟେଡ୍) – were beaten (ପରାସ୍ତ ହୋଇଥିଲେ)
documentary (ଡକ୍ୟୁମେଣ୍ଟାରୀ – a film giving facts (ତଥ୍ୟଭିଭିକ, ପ୍ରାମାଣିକ ଚଳଚ୍ଚିତ୍ର)
evil (ଏଭିଲ) – bad spirit (ଖରାପ ଆତ୍ମା, ପ୍ରେତାତ୍ମା)
gathered (ଗ୍ୟାଦର୍‌ଡ଼) – came in large number to one place (ଏକାଠି ହୋଇଥିଲେ )
innocent (ଇନୋସେଣ୍ଟ) – good and harmless people (ନିରୀହ, ନିଘୋଷ ବ୍ଯକ୍ତି)
mercilessly (ମର୍ସଲେସ୍‌ଲି) – cruelly (ଭୀଷଣ ନିର୍ଭୟ ଭାବରେ)
money lender (ମନି ଲେଣ୍ଡର) – a person who gives money to people in their need and collects it afterwards with interest (ଟଙ୍କା ସୁଧ କାରବାର କରୁଥିବା ବ୍ୟକ୍ତି)
movement (ମୁଭମେଣୁ) – mass fight to achieve something
pattas (ପଟ୍ଟାଜ୍)– land ownership papers (ଜମି ପଟ୍ଟା)
poisoned (ପଏଜନ୍‌) – (He was) given poison (ବିଷ ଦିଆଯାଇଥିଲା)
poverty (ପଭର୍ଟି) – a condition of having no money, no wealth or basic needs of life (ଦାରିଦ୍ର୍ୟ, ଗରିବ ଅବସ୍ଥା)
property (ପ୍ରପର୍ଟି) – wealth (ଧନସମ୍ପତ୍ତି)
quack – a person who does treatment of people without proper knowledge, especially in villages (ଗାଁ ବଇଦ, ଗୁଣିଆ)
religious (ରିଲିଜିଅସ୍ ) – one who shows strong faith in religion and obey its rules (ଧର୍ମନିଷ୍ଠ, ଧାର୍ମିକ)
reward (ରିୱାର୍ଡ) – wealth or money given to somebody for good work (ପୁରସ୍କାର)
sacrificed (ସାକ୍ରିଫାଇସ୍‌ଡ୍) – gave life for the cause of his country (ପାଇଁ ଜୀବନ ଉତ୍ସର୍ଗ କରିଥିଲେ)
sacrifice (ସାକ୍ରିଫାଇସ୍ ) – to give a gift of animal (goat) to god or goddess to win their favour
Santal (ସାନ୍ତାଲ) – a class of triabl (ଏକ ଆଦିବାସୀ ସମ୍ପ୍ରଦାୟ)
superstition (ସୁପରଷ୍ଟିସନ୍) – belief without based on facts, blind belief (ଅନ୍ଧବିଶ୍ଵାସ )
suspected (ସସ୍‌କୁ ଡ୍) – doubted ( ସନ୍ଦେହ ପ୍ରକଟ କରିବା)
tearful (ଟିୟରଫୁଲ୍) – sorrowful way (ଅଶୁଳ, ଦୁଃଖଦ)
weapons (ଉଇପନ୍ସ୍) – instruments used for fight like sword, gun etc. (ଅସ୍ତ୍ରଶସ୍ତ୍ର)
worship (ଓରସିପ୍ ) – pray (ପୂଜା କରିବା ବା ପ୍ରାର୍ଥନା କରିବା)
wounded (ୱିଣ୍ଡ୍ଡ୍) – injured, cut (his leg) (ହାଣି ହୋଇଯିବା, କ୍ଷତାକ୍ତ ହେବା, ଆହତ ହେବା )

BSE Odisha 7th Class English Solutions Tail-Piece Lesson Branding Babies by Hot Iron Rods-A Bad Practice Important Questions and Answers

(A) Answer the following questions.
Question 1.
Why did the people call him Tilka Baba?
Answer:
Tilka was worshiping Marang Burn. When days went by he became a religious man. The people of all religions, loved him and respected him. So they called him Tilka Baba.

Question 2.
How did Bhagalpur come under the control of the British?
Answer:
After the Plassey battle, British became the rulers of Bengal, Bihar and Odisha. So Bhagalpur of Bihar came under their control.

Question 3.
How did Cleareland tortured the natives?
Answer:
The new collector Cleareland appointed soldiers from other tribes to fight against the Santals. In many ways he tried to harash the people.

(B) Multiple Choice Questions (MCQs) with Answers.
Question 1.
Birsa Munda was born in a _________.
(a) rich family
(b) poor family
(c) joint family
(d) aristocratic family
Answer:
(b) poor family

Question 2.
His father’s name was _________.
(a) Sugana Munda
(b) Laxman Munda
(c) Sovan Munda
(d) None of these
Answer:
(a) Sugana Munda

(C) Re-arrange the jumbled words to make meaningful sentences.
Question 1.
superstition / from / days / very / Birsa / young / was / against
Answer:
From very young days Birsa was against superstition.

Question 2.
the / was / by / evil / the / said / quack / that / wound / caused / an / spirit
Answer:
The quack said that the wound was caused by an evil spirit:

Question 3.
wound / himself / his / of / to / a / cure / goat / Birsa / sacrifice / would / to / have
Answer:
Birsa would have to sacrifice a goat to cure himself of his wound.

(D) Find whether True or False.
Question 1.
Birsa Munda was born in a rich family in Odisha in 1975.
Answer:
False

Question 2.
From the very young age he worked as a cowboy of landlord.
Answer:
True

Question 3.
Birsa would have to sacrifice a hen to cure himself of his wound.
Answer:
False

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 5 Determinants Ex 5(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Exercise 5(a)

Question 1.
Evaluate the following determinants.
(i) \(\left|\begin{array}{ll}
1 & 1 \\
2 & 3
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ll}
1 & 1 \\
2 & 3
\end{array}\right|\) = 3 – 2 = 1

(ii) \(\left|\begin{array}{ll}
2 & -3 \\
1 & -4
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ll}
2 & -3 \\
1 & -4
\end{array}\right|\) = -8 + 3 = -5

(iii) \(\left|\begin{array}{ll}
\sec \theta & \tan \theta \\
\tan \theta & \sec \theta
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ll}
\sec \theta & \tan \theta \\
\tan \theta & \sec \theta
\end{array}\right|\) = sec² θ – tan² θ = 1

(iv) \(\left|\begin{array}{ll}
0 & x \\
2 & 0
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ll}
0 & x \\
2 & 0
\end{array}\right|\) = 0 – 2x = -2x

(v) \(\left|\begin{array}{cc}
1 & \omega \\
-\omega & \omega
\end{array}\right|\)
Solution:
\(\left|\begin{array}{cc}
1 & \omega \\
-\omega & \omega
\end{array}\right|\) = ω + ω² = -1

(vi) \(\left|\begin{array}{cc}
4 & -1 \\
3 & 2
\end{array}\right|\)
Solution:
\(\left|\begin{array}{cc}
4 & -1 \\
3 & 2
\end{array}\right|\) = 8 + 3 = 11

(vii) \(\left|\begin{array}{ll}
\cos \theta & \sin \theta \\
\sin \theta & \cos \theta
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ll}
\cos \theta & \sin \theta \\
\sin \theta & \cos \theta
\end{array}\right|\) = cos² θ – sin² θ = cos 2θ

(viii) \(\left|\begin{array}{lll}
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1
\end{array}\right|\)
Solution:
\(\left|\begin{array}{lll}
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1
\end{array}\right|\) = 0
as the rows are identical.

(ix) \(\left|\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right|\)
Solution:
\(\left|\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right|\) = 1\(\left|\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right|\) = 1 – 0 = 1

(x) \(\left|\begin{array}{ccc}
2 & 3 & 1 \\
0 & 0 & 0 \\
-1 & 2 & 0
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ccc}
2 & 3 & 1 \\
0 & 0 & 0 \\
-1 & 2 & 0
\end{array}\right|\) = 0
as all the entries in the 2nd row are zero.

(xi) \(\left|\begin{array}{ccc}
1 & x & y \\
0 & \sin x & \sin y \\
0 & \cos x & \cos y
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ccc}
1 & x & y \\
0 & \sin x & \sin y \\
0 & \cos x & \cos y
\end{array}\right|\) = 1\(\left|\begin{array}{cc}
\sin x & \sin y \\
\cos x & \cos y
\end{array}\right|\)
= sin x cos y – cos x sin y = sin (x – y)

(xii) \(\left|\begin{array}{lll}
1 & 2 & 3 \\
1 & 2 & 3 \\
3 & 4 & 5
\end{array}\right|\)
Solution:
\(\left|\begin{array}{lll}
1 & 2 & 3 \\
1 & 2 & 3 \\
3 & 4 & 5
\end{array}\right|\) = 0 (∵ R₁ = R₂)

(xiii) \(\left|\begin{array}{lll}
0.2 & 0.1 & 3 \\
0.4 & 0.2 & 7 \\
0.6 & 0.3 & 2
\end{array}\right|\)
Solution:
\(\left|\begin{array}{lll}
0.2 & 0.1 & 3 \\
0.4 & 0.2 & 7 \\
0.6 & 0.3 & 2
\end{array}\right|\)
= 2\(\left|\begin{array}{lll}
0.2 & 0.1 & 3 \\
0.4 & 0.2 & 7 \\
0.6 & 0.3 & 2
\end{array}\right|\) = 0 (∵ C₁ = C₂)

(xiv) \(\left|\begin{array}{ccc}
1 & \omega & \omega^2 \\
\omega & \omega^2 & 1 \\
\omega^2 & 1 & \omega
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ccc}
1 & \omega & \omega^2 \\
\omega & \omega^2 & 1 \\
\omega^2 & 1 & \omega
\end{array}\right|\)

(xv) \(\left|\begin{array}{lll}
1 & 1 & 1 \\
2 & 2 & 2 \\
3 & 3 & 3
\end{array}\right|\)
Solution:
\(\left|\begin{array}{lll}
1 & 1 & 1 \\
2 & 2 & 2 \\
3 & 3 & 3
\end{array}\right|\) = 0 (∵ C₁ = C₂)

(xvi) \(\left|\begin{array}{ccc}
-6 & 0 & 0 \\
3 & -5 & 7 \\
2 & 8 & 11
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ccc}
-6 & 0 & 0 \\
3 & -5 & 7 \\
2 & 8 & 11
\end{array}\right|\)
= (-6) \(\left|\begin{array}{cc}
-5 & 7 \\
8 & 11
\end{array}\right|\) = = (-6) (- 55 – 56)
= (-6) (-111) = 666

(xvii) \(\left|\begin{array}{lll}
1 & 0 & 0 \\
2 & 3 & 5 \\
4 & 1 & 3
\end{array}\right|\)
Solution:
\(\left|\begin{array}{lll}
1 & 0 & 0 \\
2 & 3 & 5 \\
4 & 1 & 3
\end{array}\right|\)
= 1 \(\left|\begin{array}{ll}
3 & 5 \\
1 & 3
\end{array}\right|\) = 9 – 5 = 4

(xviii) \(\left|\begin{array}{ccc}
-18 & 17 & 19 \\
3 & 0 & 0 \\
-14 & 5 & 2
\end{array}\right|\)
Solution:
\(\left|\begin{array}{ccc}
-18 & 17 & 19 \\
3 & 0 & 0 \\
-14 & 5 & 2
\end{array}\right|\)
= -3 \(\left|\begin{array}{cc}
17 & 19 \\
5 & 2
\end{array}\right|\)
(Expanding along 2nd row)
= – 3 (34 – 95)
= (-3) (-61) = 183

Question 2.
State true or false.
(i) If the first and second rows of a determinant be interchanged then the sign of the determinant is changed.
Solution:
True

(ii) If first and third rows of a determinant be interchanged then the sign of the determinent does not change.
Solution:
False

(iii) If in a third order determinant first row be changed to second column. Second row to 1st column and third row to third column, then the value of the determinant does not change.
Solution:
False

(iv) A row and a column of a determinant can have two or more common elements.
Solution:
False

(v) The minor and the co-factor of the element a₃₂ of a determinant of third order are equal.
Solution:
False

(vi) \(\left|\begin{array}{lll}
3 & 1 & 3 \\
0 & 4 & 0 \\
1 & 3 & 1
\end{array}\right|\) = 0
Solution:
True

(vii) \(\left|\begin{array}{lll}
6 & 4 & 2 \\
4 & 0 & 7 \\
5 & 3 & 4
\end{array}\right|\) = \(\left|\begin{array}{lll}
6 & 4 & 5 \\
4 & 0 & 3 \\
2 & 7 & 3
\end{array}\right|\)
Solution:
True

(viii) \(\left|\begin{array}{lll}
2 & 3 & 4 \\
5 & 6 & 7 \\
1 & 2 & 3
\end{array}\right|\) = \(\left|\begin{array}{lll}
4 & 2 & 3 \\
7 & 5 & 6 \\
3 & 1 & 2
\end{array}\right|\)
Solution:
True

Question 3.
Fill in the blanks with appropriate answer from the brackes.
(i) The value of \(\left|\begin{array}{ccc}
0 & 8 & 0 \\
25 & 520 & 25 \\
1 & 410 & 0
\end{array}\right|\) = _______. (0, 25, 200, -250)
Solution:
200

(ii) If ω is the cube root of unity, then \(\left|\begin{array}{ccc}
1 & \omega & \omega^2 \\
\omega & \omega^2 & 1 \\
\omega^2 & 1 & \omega
\end{array}\right|\) = _______. (1, 0, ω, ω²)
Solution:
0

(iii) The value of the determinant \(\left|\begin{array}{lll}
1 & a & b+c \\
1 & b & c+a \\
1 & c & a+b
\end{array}\right|\) = _______. (a + b – c, (a + b + c)², 0, 1 + a + b + c)
Solution:
0

(iv) If \(\left|\begin{array}{lll}
a & b & c \\
b & a & b \\
x & b & c
\end{array}\right|\) = 0, then x = _______. (a, b, c, a + b + c)
Solution:
a

(v) \(\left|\begin{array}{lll}
a_1+a_2 & a_3+a_4 & a_5 \\
b_1+b_2 & b_3+b_4 & b_5 \\
c_1+c_2 & c_3+c_4 & c_5
\end{array}\right|\) can be expressed at the most as _______, different 3rd order determinants. (1, 2, 3, 4)
Solution:
4

(vi) Minimum value of \(\left|\begin{array}{cc}
\sin x & \cos x \\
-\cos x & 1+\sin x
\end{array}\right|\) is _______. (-1, 0, 1, 2)
Solution:
0

(vii) The determinant \(\left|\begin{array}{lll}
1 & 1 & 1 \\
1 & 2 & 3 \\
1 & 3 & 6
\end{array}\right|\) is not equal to _______. \(\left(\left|\begin{array}{lll}
2 & 1 & 1 \\
2 & 2 & 3 \\
2 & 3 & 6
\end{array}\right|,\left|\begin{array}{lll}
2 & 1 & 1 \\
3 & 2 & 3 \\
4 & 3 & 6
\end{array}\right|,\left|\begin{array}{lll}
1 & 2 & 1 \\
1 & 5 & 3 \\
1 & 9 & 6
\end{array}\right|,\left|\begin{array}{ccc}
3 & 1 & 1 \\
6 & 2 & 3 \\
10 & 3 & 6
\end{array}\right|\right)\)
Solution:
\(\left|\begin{array}{lll}
2 & 1 & 1 \\
2 & 2 & 3 \\
2 & 3 & 6
\end{array}\right|\)

(viii) With 4 different elements we can construct _______ number of different determinants of order 2. (1, 6, 8, 24)
Solution:
6

Question 4.
Solve the following:
(i) \(\left|\begin{array}{cc}
4 & x+1 \\
3 & x
\end{array}\right|\)
Solution:
\(\left|\begin{array}{cc}
4 & x+1 \\
3 & x
\end{array}\right|\) = 5
or, 4x – 3x – 3 = 5 or, x = 8

(ii) \(\left|\begin{array}{ccc}
\boldsymbol{x} & a & a \\
m & m & m \\
b & x & b
\end{array}\right|\) = 0
Solution:

(Replacing C₁ and C₂ by C₁ – C₃ and C₂ – C₃ respectively)
⇒ m |(x – a) (-x + b)| = 0
⇒ m (x – a) (b – x) – 0 ⇒ x = a, b

(iii) \(\left|\begin{array}{lll}
7 & 6 & x \\
2 & x & 2 \\
x & 3 & 7
\end{array}\right|\) = 0
Solution:

or, (x – 7) (7x + x² – 1 8) = 0
or, (x – 7) (x² + 7x – 18) = 0
or, (x – 7) (x + 9) (x – 2) = 0
∴ x = -9, 2, 7

(iv) \(\left|\begin{array}{ccc}
0 & x-a & x-b \\
x+a & 0 & x-c \\
x+b & x+c & 0
\end{array}\right|\) = 0
Solution:

or, – (x – a) {0 – (x + b) (x – c)} + (x – b) (x + a) (x + c) = 0
or, (x – a) (x + b) (x – c) + (x – b) (x + a) (x + c) = 0
or, (x² + bx – ax – ab) (x – c) + (x² + ax – bx – ab) (x + c) = 0
or, x³ – cx² + bx² – bcx – ax² + acx – abx + abc + x³ + cx² + ax² + acx- bx² – bcx – abx – abc = 0
or, 2x³ – 2abx – 2bcx + 2acx = 0
or, 2x (x² – ab – bc + ac) = 0
x = 0, x² = ab + bc – ca
∴ x = 0, x = \(\sqrt{a b+b c-c a}\)

(v) \(\left|\begin{array}{ccc}
\boldsymbol{x}+\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\
\boldsymbol{b} & \boldsymbol{x}+\boldsymbol{c} & \boldsymbol{a} \\
\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{x}+\boldsymbol{b}
\end{array}\right|\) = 0
Solution:

⇒ (x + a + b + c) {x² + bx + cx + bc – a² – bx – b² + ca + ab – cx – c² = 0}
⇒ (x + a + b + c) {x² – a² – b² – c² + ab + bc + ca} = 0
⇒ x + a + b + c = 0
or, x² – a² – b² – c² + ab + bc + ca = 0
⇒ x = – (a + b + c)
∴ or x = \(\sqrt{a^2+b^2+c^2-a b-b c-c a}\)

(vi) \(\left|\begin{array}{ccc}
1+x & 1 & 1 \\
1 & 1+x & 1 \\
1 & 1 & 1+x
\end{array}\right|\) = 0
Solution:

(vii) \(\left|\begin{array}{ccc}
1 & 4 & 20 \\
1 & -2 & 5 \\
1 & 2 x & 5 x^2
\end{array}\right|\) = 0
Solution:

⇒ -30x² + 30 + 30x + 30 = 0
⇒ -30x² + 30x + 60 = 0
⇒ x² – x – 2 = 0
⇒ x² – 2x + x + 2 = 0
⇒ (x – 2) (x + 1) = 0
⇒ x = 2, -1

(viii) \(\left|\begin{array}{ccc}
x+1 & \omega & \omega^2 \\
\omega & x+\omega^2 & 1 \\
\omega^2 & 1 & x+\omega
\end{array}\right|\) = 0
Solution:

⇒ x(x² + xω – xω² + xω² + ω³ – ω⁴ – xω – ω² + ω³ – 1 + ω² + ω – ω³) = 0
⇒ x(x² + ω³ – ω⁴ – ω² + ω³ – 1 + ω² + ω – ω³) = 0
⇒ x(x² + ω³ – ω + ω – 1) = 0
⇒ x(x² + 1 – ω + ω – 1) = 0 (∵ ω³ = 1)
⇒ x³ = 0
⇒ x = 0

(ix) \(\left|\begin{array}{ccc}
2 & 2 & x \\
-1 & x & 4 \\
1 & 1 & 1
\end{array}\right|\) = 0
Solution:

or, 10 + 10x – x² – 8x – x – 8 = 0
or, x² – 2x + x – 2 = 0
or, (x – 2) (x + 1) = 0
x = 2, x = -1

(x) \(\left|\begin{array}{lll}
x & 1 & 3 \\
1 & x & 1 \\
3 & 6 & 3
\end{array}\right|\) = 0
Solution:

or, x(3x – 6) – 0 + 3(6 – 3x) = 0
or, 3x² – 6x + 18 – 9x = 0
or, 3x² – 15x + 18 = 0
or, x² – 5x + 6 = 0
or, (x – 3) (x – 2) = 0
x = 3 or, x = 2

Question 5.
Evaluate the following
(i) \(\left|\begin{array}{ccc}
2 & 3 & 4 \\
1 & -1 & 3 \\
4 & 1 & 10
\end{array}\right|\)
Solution:

(ii) \(\left|\begin{array}{lll}
\boldsymbol{x} & \mathbf{1} & 2 \\
\boldsymbol{y} & \mathbf{3} & 1 \\
z & 2 & 2
\end{array}\right|\)
Solution:

(iii) \(\left|\begin{array}{ccc}
x & 1 & -1 \\
2 & y & 1 \\
3 & -1 & z
\end{array}\right|\)
Solution:

= x (yz + z – z + 1) – (2z – 2 – 3y – 3)
= xyz + x – 2z + 3y + 5
= xyz + x + 3y – 2z + 5

(iv) \(\left|\begin{array}{lll}
a & h & g \\
h & b & f \\
g & f & c
\end{array}\right|\)
Solution:

= a(bc – f²) – h (ch – fg) + g (hf – bg)
= abc – af² – ch² + fgh + fgh – bg²
= abc + 2fgh – af² – bg² – ch²

(v) \(\left|\begin{array}{lll}
a & h & g \\
h & b & f \\
g & f & c
\end{array}\right|\)
Solution:

(vi) \(\left|\begin{array}{ccc}
\sin ^2 \theta & \cos ^2 \theta & 1 \\
\cos ^2 \theta & \sin ^2 \theta & 1 \\
-10 & 12 & 2
\end{array}\right|\)
Solution:

(vii) \(\left|\begin{array}{ccc}
-1 & 3 & 2 \\
1 & 3 & 2 \\
1 & -3 & -1
\end{array}\right|\)
Solution:

(viii) \(\left|\begin{array}{ccc}
11 & 23 & 31 \\
12 & 19 & 14 \\
6 & 9 & 7
\end{array}\right|\)
Solution:

(ix) \(\left|\begin{array}{ccc}
37 & -3 & 11 \\
16 & 2 & 3 \\
5 & 3 & -2
\end{array}\right|\)
Solution:

(x) \(\left|\begin{array}{ccc}
2 & -3 & 4 \\
-4 & 2 & -3 \\
11 & -15 & 20
\end{array}\right|\)
Solution:

= 2(40 – 45) + 3(-80 + 33) + 4(60 – 22)
= -10 – 141 + 152 = -151 + 152 = 1

Question 6.
Show that x = 1 is a solution of \(\left|\begin{array}{ccc}
x+1 & 3 & 5 \\
2 & x+2 & 5 \\
2 & 3 & x+4
\end{array}\right|\) = 0
Solution:

or, (x + 9) {(x – 1)²} – 0
or, x = -9, 1
∴ x = 1 is a solution of the given equation.

Question 7.
Show that (a + 1) is a factor of \(\left|\begin{array}{ccc}
a+1 & 2 & 3 \\
1 & a+1 & 3 \\
3 & -6 & a+1
\end{array}\right|\) = 0
Solution:

= (a+ 1) {(a + 1)² + 18} – 2(a + 1 – 9) + 3(- 6 – 3a – 3)
= (a + 1) (a² + 2a + 1 + 18) – 2(a – 8) + 3(- 9 – 3a)
= (a + 1) (a² + 2a + 19) – 2a + 16 – 27 – 9a
= (a + 1) (a² + 2a + 19) – 11a – 11
= (a + 1) (a² + 2a + 19) – 11(a + 1)
= (a + 1) (a² + 2a + 19 – 11)
= (a + 1) (a² + 2a + 8)
∴ (a + 1) is a factor of the above determinant.

Question 8.
Show that \(\left|\begin{array}{ccc}
a_1 & b_1 & -c_1 \\
-a_2 & b_2 & c_2 \\
a_3 & b_3 & -c_3
\end{array}\right|=\left|\begin{array}{lll}
a_1 & b_1 & c_1 \\
a_2 & b_2 & c_2 \\
a_3 & b_3 & c_3
\end{array}\right|\)
Solution:

Question 9.
Prove the following
(i) \(\left|\begin{array}{lll}
a & b & c \\
\boldsymbol{x} & y & z \\
\boldsymbol{p} & q & r
\end{array}\right|=\left|\begin{array}{lll}
\boldsymbol{y} & \boldsymbol{b} & \boldsymbol{q} \\
\boldsymbol{x} & \boldsymbol{a} & p \\
z & c & r
\end{array}\right|=\left|\begin{array}{lll}
\boldsymbol{x} & \boldsymbol{y} & z \\
\boldsymbol{p} & \boldsymbol{q} & r \\
a & b & c
\end{array}\right|\)
Solution:

(ii) \(\left|\begin{array}{ccc}
1+a & 1 & 1 \\
1 & 1+b & 1 \\
1 & 1 & 1+c
\end{array}\right|\) = abc \(\left(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
Solution:

(iii) \(\left|\begin{array}{lll}
b+c & c+a & a+b \\
q+r & r+p & p+q \\
y+z & z+x & x+y
\end{array}\right|=2\left|\begin{array}{lll}
a & b & c \\
p & q & r \\
x & y & z
\end{array}\right|\)
Solution:

(iv) \(\left|\begin{array}{lll}
(a+1)(a+2) & a+2 & 1 \\
(a+2)(a+3) & a+3 & 1 \\
(a+3)(a+4) & a+4 & 1
\end{array}\right|\) = -2
Solution:

(v) \(\left|\begin{array}{ccc}
a+d & a+d+k & a+d+c \\
c & c+b & c \\
d & d+k & d+c
\end{array}\right|\) = abc
Solution:

(vi) \(\left|\begin{array}{ccc}
1 & 1 & 1 \\
b+c & c+a & c+a \\
b^2+c^2 & c^2+a^2 & a^2+b^2
\end{array}\right|\) = (b – c) (c – a) (a – b)
Solution:

(vii) \(\left|\begin{array}{lll}
a & a^2 & a^3 \\
b & b^2 & b^3 \\
c & c^2 & c^3
\end{array}\right|\) = abc (a – b) (b – c) (c – a)
Solution:

(viii) \(\left|\begin{array}{ccc}
\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{a} \\
\boldsymbol{b} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}
\end{array}\right|\) = 4abc
Solution:

= (b + c – a) {(a + b) (c + a – b) – b (c – a – b)} + a (b – c – a) (c – a – b)
= (b + c – a)(ca + a² – ab + bc + ab – b² – bc + ab + b²) + a(bc – ab – b² – c² + ca + bc – ac + a² + ab)
= (b + c – a) (a² + ab + ca) + a (a² – b² – c² + 2bc)
= a²b + ab² + abc + ca² + abc + c²a – a³ – a²b – ca² + a³ – b²a – c²a + 2abc = 4abc

(ix) \(\left|\begin{array}{ccc}
b^2+c^2 & a b & a c \\
a b & c^2+a^2 & b c \\
c a & c b & a^2+b^2
\end{array}\right|\) = 4a²b²c²
Solution:

(x) \(\left|\begin{array}{ccc}
a & b & c \\
a^2 & b^2 & c^2 \\
b c & c a & a b
\end{array}\right|\) = (b – c) (c – a) (a – b) (bc + ca + ab)
Solution:

= (a – b) (b – c) (c – a) – (- ab + c²) + c (a + b + c)
= (a – b) (b – c) (c – a) (ab – c² + ca + bc + c²)
= (a – b) (b – c) (c – a) (ab + bc + ca)

(xi) \(\left|\begin{array}{ccc}
a-b-c & 2 a & 2 a \\
2 b & b-c-a & 2 b \\
2 c & 2 c & c-a-b
\end{array}\right|\) = (a + b+ c)³
Solution:

(xii) \(\left|\begin{array}{ccc}
(v+w)^2 & u^2 & u^2 \\
v^2 & (w+u)^2 & v^2 \\
w^2 & w^2 & (u+v)^2
\end{array}\right|\) = 2uvw (u + v + w)³
Solution:

Question 10.
Factorize the following
(i) \(\left|\begin{array}{ccc}
x+a & b & c \\
b & x+c & a \\
c & a & x+b
\end{array}\right|\)
Solution:

= (x + a + b + c) [(x + c – b) (x + b – a) – (a – c) (a – x – c)]
= (x + a + b + c) (x² + xb – ax + cx +bc – ca – bx – b² + ab – a² + ax + ac + ac – cx – c²)
= (x + a + b + c) (x² – a² – b² – c² + ab + bc + ca)

(ii) \(\left|\begin{array}{ccc}
a & b & c \\
b+c & c+a & a+b \\
a^2 & b^2 & c^2
\end{array}\right|\)
Solution:

(iii) \(\left|\begin{array}{ccc}
x & 2 & 3 \\
1 & x+1 & 3 \\
1 & 4 & x
\end{array}\right|\)
Solution:

Question 11.
Show that by eliminating α and from the equations.
a_i α + b_i β + c_i = 0, i = 1, 2, 3 we get \(\left|\begin{array}{lll}
a_1 & b_1 & c_1 \\
a_2 & b_2 & c_2 \\
a_2 & b_3 & c_3
\end{array}\right|\) = 0
Solution:
We have
a₁ α + b₁ β + c₁ = 0    …..(1)
a₂ α + b₂ β + c₂ = 0    …..(2)
a₃ α + b₃ β + c₃ = 0    …..(3)
Solving (2) and (3) by cross-multiplication method we have

Question 12.
Prove the following:
(i) \(\left|\begin{array}{lll}
1 & b c & a(b+c) \\
1 & c a & b(c+a) \\
1 & a b & c(a+b)
\end{array}\right|\) = 0
Solution:

(ii) \(\left|\begin{array}{ccc}
x+4 & 2 x & 2 x \\
2 x & x+4 & 2 x \\
2 x & 2 x & x+4
\end{array}\right|\) = (5x + 4) (4- x)²
Solution:

(iii) \(\left|\begin{array}{l}
\sin \alpha \cos \alpha \cos (\alpha+\delta) \\
\sin \beta \cos \beta \cos (\beta+\delta) \\
\sin \alpha \cos \gamma \cos (\gamma+\delta)
\end{array}\right|\) = 0
Solution:

(iv) \(\left|\begin{array}{ccc}
1 & x & x^2 \\
x^2 & 1 & x \\
x & x^2 & 1
\end{array}\right|\) = (1 -x³)²
Solution:

Question 13.
Prove that the points (x₁, y₁), (x₂, y₂), (x₃, y₃) are collinear if \(\left|\begin{array}{lll}
x_1 & y_1 & 1 \\
x_2 & y_2 & 1 \\
x_3 & y_3 & 1
\end{array}\right|\) = 0
Solution:
From geometry, we know that, if the points A, B, C, are collinear, then the area of the triangle ABC with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is zero.
\(\left|\begin{array}{lll}
x_1 & y_1 & 1 \\
x_2 & y_2 & 1 \\
x_3 & y_3 & 1
\end{array}\right|\) = 0

Question 14.
If A + B + C = π, prove that \(\left|\begin{array}{lll}
\sin ^2 A & \cot A & 1 \\
\sin ^2 B & \cot B & 1 \\
\sin ^2 C & \cot C & 1
\end{array}\right|\) = 0
Solution:

Question 15.
Eliminate x, y, z from a = \(\frac{x}{y-z}\), b = \(\frac{y}{z-x}\), c = \(\frac{z}{x-y}\)
Solution:
We have
a = \(\frac{x}{y-z}\), b = \(\frac{y}{z-x}\), c = \(\frac{z}{x-y}\)
ay – az – x = 0, bz – bx – y = 0, cx – cy – z = 0
x – ay + az = 0
bx + y – bz = 0
cx – cy – z = 0
Now eliminating x, y, z from the above equations we have,

or, – 1 – bc + a(-b + bc) + a(-bc – c) = 0
or, – 1 – bc – ab + abc – abc – ac = 0
or, ab + bc + ca + 1 = 0

Question 16.
Given the equations
x = cy + bz, y = az + ex and z = bx + ay where x, y and z are not all zero, prove that a² + b² + c² + 2abc = 1 by determinant method.
Solution:
x = cy + bz, y = az + cx and z = bx + ay

or, 1 – a² + c(-c – ab) – b(ca + b) = 0
or, 1 – a² – c² – abc – abc – b² = 0
or, a² + b² + c² + 2abc = 1

Question 17.
If ax + hy + g = 0, hx + by +f = 0 and gx + fy + c = λ, find the value of λ, in the form of a determinant.
Solution:

Odisha State Board BSE Odisha 7th Class English Solutions Follow-Up Lesson 2 A Tiny Warrior When I Grow Up Textbook Exercise Questions and Answers.

BSE Odisha Class 7 English Solutions Follow-Up Lesson 2 A Tiny Warrior

BSE Odisha 7th Class English Follow-Up Lesson 2 A Tiny Warrior Text Book Questions and Answers

Session – 1 (ଶବ୍ଦାବଳୀ)

I. Pre-Reading (ପୂର୍ବ ପ୍ରସ୍ତୁତି)

• Socialization (ସାମାଜିକୀକରଣ):
• In the main lesson the father learned a lesson from his son. The son taught the father that the poor people are. in fact, rich. In this follow-up lesson you will read about a small girl of class-V leading a movement against bazzar notebooks. Let’s read and see how cheap bazaar notebooks do more harm than good.

II. While Reading (ପଠନକାଳୀନ)
Text(ପାଠ୍ୟବସ୍ତୁ)

• SGP-1 (Sense Group Paragraph-1)
• Read paragraph 1 and 2 and answer the questions.
  (ଅନୁଚ୍ଛେଦ ୧ ଓ ୨କୁ ନୀରବରେ ପାଠ କର ଏବଂ ନିମ୍ନ ପ୍ରଶ୍ନଗୁଡ଼ିକର ଉତ୍ତର ଦିଅ ।)

1. One evening Mitu and Situ, two sisters, were studying in their room. Mitu studies in class VII and Situ in Class V. The two sisters were studying in two different schools. Their uncle, Mr. Giri, was watching them from a little distance. He was a retired teacher. He had come to visit them on a week-end. Mr. Giri saw Mitu reading one paragraph from her English textbook then reading the meaning of this paragraph in Odia from a bazaar notebook (Meaning book), which disturbed him. ‘If children study English like this, they will never learn English’, he thought.

2. The uncle was eager to help Mitu learn English on her own without the help of this meaning book. He came close to her and asked her to read the first paragraph of the lesson silently. The lesson was “The Story of Cricket”. The first paragraph was: The shape and the size of a cricket ground are not fixed. They are different. The cricket ground of Melbourne in Australia is bigger than that of Feroz Shah Kotla in New Delhi. Similarly the shape of Chepauk Cricket Ground in Chennai is circular. But the Adelaide Cricket Ground in Australia is oval.

ଓଡ଼ିଆ ଅନୁବାଦ :
୧. ଦିନେ ସନ୍ଧ୍ୟାରେ ମିତୁ ଏବଂ ସିତୁ ଦୁଇ ଭଉଣୀ ସେମାନଙ୍କ ପଢ଼ାଘରେ ପଢ଼ା କାର୍ଯ୍ୟ କରୁଥିଲେ । ମିତୁ ୭ମ ଶ୍ରେଣୀରେ ଏବଂ ସିତୁ ୫ମ ଶ୍ରେଣୀରେ ପଢ଼େ । ଦୁଇ ଭଉଣୀ ଦୁଇଟି ଅଲଗା ସ୍କୁଲରେ ପାଠ ପଢୁଥିଲେ । ସେମାନଙ୍କ ଦାଦା/ ମାମୁ ଗିରିବାବୁ ସେମାନଙ୍କୁ କିଛି ଦୂରରୁ ଲକ୍ଷ୍ୟ କରୁଥିଲେ । ସେ ଜଣେ ଅବସରପ୍ରାପ୍ତ ଶିକ୍ଷକ । ସପ୍ତାହର ଶେଷ ଦିନରେ ସେ ତାଙ୍କୁ ଦେଖିବାକୁ ଆସିଥିଲେ । ଗିରିବାବୁ ଦେଖ‌ିଲେ ମିତ୍ରୁ ତା’ ଇଂରାଜୀ ପାଠ୍ୟପୁସ୍ତକର ଏକ ଅନୁଚ୍ଛେଦ ପଢ଼ୁଥିଲା ଏବଂ ପରେ ପରେ ସେହି ଅନୁଚ୍ଛେଦର ଓଡ଼ିଆ ଅନୁବାଦ ବଜାରରୁ ଖରିଦ କରିଥିବା ଏକ ମାନେ ବହିରୁ ପଢ଼ୁଥିଲା । ତାହା ତାଙ୍କୁ ବଡ଼ ଅଡୁଆ ଲାଗିଲା । ସେ ଭାବିଲେ- ଯଦି ପିଲାମାନେ ଇଂରାଜୀ ଏଭଳି ଢଙ୍ଗରେ ପଢ଼ିବେ, ସେମାନେ ଇଂରାଜୀ ଶିକ୍ଷା କରିପାରିବେ ନାହିଁ ।

୨.ଦାଦା/ମାମୁ ଜଣକ ମିତୁ କିଭଳି ଆପେ ଆପେ ମାନେ ବହି ବିନା ଇଂରାଜୀ ଶିକ୍ଷା କରିପାରିବ, ସେ ସମ୍ବନ୍ଧରେ ସାହାଯ୍ୟ କରିବାକୁ ବ୍ୟଗ୍ର ହୋଇଉଠିଲେ । ସେ ତା’ ପାଖକୁ ଆସିଲେ ଏବଂ ପ୍ରଥମ ଅନୁଚ୍ଛେଦଟିକୁ ନୀରବରେ ପାଠ କରିବାକୁ କହିଲେ । ପାଠ୍ୟବସ୍ତୁଟି ଥୁଲା ‘କ୍ରିକେଟ୍‌ର ଏକ କାହାଣୀ ।’ ପ୍ରଥମ ଅନୁଚ୍ଛେଦଟି ଏହିପରି ଥୁଲା ମେଲ୍‌ବର୍ଷ କ୍ରିକେଟ୍ ପଡ଼ିଆ, ନୂଆଦିଲ୍ଲୀର ଫିରୋଜ ଶାହା କୋଟଲା କ୍ରିକେଟ୍‌ ପଡ଼ିଆ ତୁଳନାରେ ବଡ଼ । ସେହିଭଳି ଚେନ୍ନାଇର ଚେପକ୍ କ୍ରିକେଟ୍ ପଡ଼ିଆର ଆକାର ଗୋଲାକାର । କିନ୍ତୁ ଅଷ୍ଟ୍ରେଲିଆର ଆଡିଲେଡ୍ କ୍ରିକେଟ୍‌ ପଡ଼ିଆ ଅଣ୍ଡାକୃତିର ।

Notes And Glossary: (ଶବ୍ଦାର୍ଥ) :
studying (ଷ୍ଟଡ଼ିଙ୍ଗ୍) – ପଢ଼ିବା
uncle (ଅଙ୍କଲ୍) – ଦାଦା | ମାମୁ
watching (ଚିଙ୍ଗ୍) – ଦେଖିବା
little distance (ଲିଟିଲ୍‌ ଡିଷ୍ଟାନ୍‌ସ୍) – ଅଳ୍ପ ଦୂର
retired teacher (ରିଟାୟାର୍ଡ ଟିଚର) – ଅବସରପ୍ରାପ୍ତ ଶିକ୍ଷକ
paragraph (ପାରାଗ୍ରାଫ୍) – ଅନୁଚ୍ଛେଦ
disturbed (ଡିଷ୍ଟବର୍ଡ) – ବିଚଳିତ ହେଲେ
eager to help (ଇଗର୍ ଟୁ ହେଲ୍ପ) – ସାହାଯ୍ୟ ପାଇଁ ଆଗ୍ରହ ପ୍ରକାଶ କରିବା
shape (ସେପ୍) – ଆକାର
size (ସାଇଜ୍) — ପ୍ରକାର, ଲମ୍ବ ପ୍ରସ୍ଥର ଦୂରତ୍ୱ
circular (ସର୍କୁଲାର) – ଗୋଲାକାର
oval (ଓଭାଲ୍) – ଅଣ୍ଡାକୃତି

Comprehension Questions (ବୋଧପରିମାପକ ପ୍ରଶ୍ନବଳୀ)

Question 1.
Who are there in paragraph X?
(ପ୍ରଥମ ଅନୁଚ୍ଛେଦରେ କିଏ କିଏ ଅଛନ୍ତି ?)
Answer:
In paragraph 1, there are two children Mitu and Situ. Their uncle Mr. Giri was with them.

Question 2.
Who are Mitu and Situ?
(ମିତୁ ଏବଂ ସିତୁ କିଏ ?)
Answer:
Mitu and Situ are two sisters. Mitu studies in class VII and Situ in class V. They were reading in different schools.

Question 3.
Who visited them on a week-end?
(ସପ୍ତାହ ଶେଷରେ କିଏ ସେମାନଙ୍କୁ ସାକ୍ଷାତ କରିବାକୁ ଆସିଥିଲେ ?)
Answer:
Mr. Giri, their uncle, visited them on a weak-end.

Question 4.
What was Mr. Giri?
(ମି. ଗିରି କ’ଣ ଥିଲେ ?)
Answer:
Mr. Giri was a retired teacher. He was the uncle of Mitu and Situ.

Question 5.
What did Mr Giri see?
(ମି. ଗିରି କ’ଣ ଦେଖ‌ିଲେ ?)
Answer:
Mr. Giri saw Mitu reading a paragraph from English textbook and then reading the meaning of the paragraph from a bazaar meaning book.

Question 6.
What was Mitu reading?
(ମିତ୍ର କ’ଣ ପଢ଼ୁଥିଲା ?).
Answer:
Mitu was reading a paragraph from English textbook.

Question 7.
Why was her uncle disturbed?
(ମାମୁଙ୍କୁ କାହିଁକି ଅଡୁଆ ଲାଗିଲା ?)
Answer:
Her uncle was disturbed because he did not like learning English taking help of bazaar notebook.

Question 8.
What did her uncle ask her?
(ତା’ ମାମୁ ତାକୁ କ’ଣ କହିଲେ ?)
Answer:
Her uncle asked her to read the first paragraph of the lesson silently.

Question 9.
What was the title of the lesson?
(ପାଠର ଶିରୋନାମା କ’ଣ ଥିଲା ?)
Answer:
The title of the lesson was “The Story of Cricket”.

Question 10.
What was the first paragraph of the lesson about?
(ଅଧ୍ୟାୟର ପ୍ରଥମ ଅନୁଚ୍ଛେଦଟି କେଉଁ ବିଷୟରେ ଥିଲା ?)
Answer:
The first paragraph of the lesson was about the shape and size of cricket ground.

Question 11.
How is this paragraph in your English book different from the paragraph in the meaning book?
(ତୁମ ଇଂରାଜୀ ବହିର ଏହି ଅନୁଚ୍ଛେଦଟି କିପରି ମାନେ ବହିର ଅନୁଚ୍ଛେଦଠାରୁ ଭିନ୍ନ ଥିଲା ?)
Answer:
This paragraph from the English book teaches how to learn and improve the knowledge in English but the paragraph from meaning book only teaches what is the meaning of the paragraph.

Session – 2 (ଦ୍ଵିତୀୟ ପର୍ଯ୍ୟାୟ)

• SGP-2 (Sense Group Paragraph-2)
• Read paragraphs – 3 to 5 and answer the questions that follow.
  (ଅନୁଚ୍ଛେଦ ୩ ରୁ ୫କୁ ପାଠ କର ଏବଂ ନିମ୍ନପ୍ରଦତ୍ତ ପ୍ରଶ୍ନଗୁଡ଼ିକର ଉତ୍ତର ଦିଅ ।)

3. Next what happened between the uncle and the niece is stated below :
Mr Giri: Every paragraph has an idea or a topic. Can you tell me the line where the topic is? What is the paragraph about? (Mitu was silent) It is about the shape and size of a cricket ground.
Mitu: The first sentence.
Mr. Giri Very Good: After telling the topic, the writer gives examples/ facts to explain the topic. Can you say what example does the writer give?
Mitu: Melbourne and Feroz Shah Kotla.
Mr Giri: Where is Melbourne cricket ground and where is Feroz Saha Kotla?
Mitu: (Reading the paragraph again) In Australia and Delhi.
Mr Giri: Very Good. Which ground is bigger in size?
Mitu: Melbourne.
Mr Giri: Good. This is about the size. What about the shape? Which ground is circular-like a circle?
Mitu: Chepauk Ground.
Mr Giri: Where is Chepauk Ground?
Mitu: In Chennai.
Mr Giri: Good. Which ground is oval shaped?
Mitu: Adelaide Ground.
Mr Giri: Where is Adelaide Ground?
Mitu: In Australia.

4. Next, the uncle asked his niece Mitu to give her notebook and on her notebook he made a note on the paragraph. The note was as follows:

5. “Now you can understand the paragraph much better. The meaning book only gives the meaning in Odia. It is not useful in learning English properly.” said Mr. Giri.

(ଓଡ଼ିଆ ଅନୁବାଦ)
୩. ତା’ପରେ ମାମୁ ଭାଣିଜୀଙ୍କ ମଧ୍ୟରେ ଯାହା ଘଟିଲା ତାହା ନିମ୍ନରେ ଉଲ୍ଲେଖ କରାଯାଇଛି :
ଶ୍ରୀ ଗିରି: ପ୍ରତ୍ୟେକ ଅନୁଚ୍ଛେଦର ଏକ ଧାରଣା ବା ବିଷୟବସ୍ତୁ ଥାଏ । କେଉଁ ଧାଡ଼ିରେ ବିଷୟବସ୍ତୁ ଅଛି ତୁମେ ମୋତେ କହିପାରିବ ବି ? ଅନୁଚ୍ଛେଦଟି କେଉଁ ବିଷୟରେ ?
ମିଟୁ: ପ୍ରଥମ ବାକ୍ୟ ।
ଶ୍ରୀ ଗିରି: ବହୁତ ଭଲ । ବିଷୟବସ୍ତୁ କହିସାରିବା ପରେ ଲେଖକ ବିଷୟବସ୍ତୁକୁ ବୁଝାଇବା ନିମନ୍ତେ ତୁମେ କହିପାରିବ କି ?
ମିଟୁ: ମେଲବୋର୍ଡ଼ ଏବଂ ଫିରୋହ ଶାହା କୋଟ୍‌ ।
ଶ୍ରୀ ଗିରି: ମେଲବୋର୍ଡ଼ କ୍ରିକେଟ୍ ପଡ଼ିଆ କେଉଁଠାରେ ଏବଂ ଫିରୋଜ ଶାହା କୋଟ୍‌ଲା କେଉଁଠାରେ ?
ମିଟୁ: (ଅନୁଚ୍ଛେଦକୁ ଆଉଥରେ ପଢ଼ି) ଅଷ୍ଟ୍ରେଲିଆ ଏବଂ ଦିଲ୍ଲୀରେ ।
ଶ୍ରୀ ଗିରି: ବହୁତ ଭଲ । କେଉଁ ପଡ଼ିଆଟି ଆକାରରେ ବଡ଼ ?
ମିଟୁ: ମେଲବୋର୍ଡ଼ ।
ଶ୍ରୀ ଗିରି: ଭଲ । ଏହା ଆକାର ବିଷୟରେ । ଆକୃତି ବିଷୟରେ କ’ଣ ? କେଉଁ ପଡ଼ିଆଟି ବୃତ୍ତାକାର – ଏକ ବୃତ୍ତ ଭଳି ।
ମିଟୁ: ଚେପକ୍ ପଡ଼ିଆ ।
ଶ୍ରୀ ଗିରି: ଚେପକ୍ ପଡ଼ିଆ କେଉଁଠାରେ ?
ମିଟୁ: ଚେନ୍ନାଇରେ ।
ଶ୍ରୀ ଗିରି:ଭଲ । କେଉଁ ପଡ଼ିଆଟି ଅଣ୍ଡାକୃତି ?
ମିଟୁ:ଆଡ଼ିଲେଡ଼ ପଡ଼ିଆ ।
ଶ୍ରୀ ଗିରି:ଆଡ଼ିଲେଡ଼ ପଡ଼ିଆ କେଉଁଠାରେ ?
ମିଟୁ:ଅଷ୍ଟ୍ରେଲିଆରେ ।

୪.ତା’ପରେ ମାମୁ ତାଙ୍କ ଭାଣିଜୀ ମିତ୍ରୁକୁ ତା’ ଖାତା ମାଗିଲେ ଏବଂ ତା’ ଖାତାରେ ଅନୁଚ୍ଛେଦର ସାରାଂଶ ଲେଖୁ ଦେଲେ । ସାରାଂଶଟି ନିମ୍ନ ପ୍ରକାର ଥିଲା :

୫. ଗିରିବାବୁ କହିଲେ, ‘ତୁମେ ବର୍ତ୍ତମାନ ଅନୁଚ୍ଛେଦଟିକୁ ଭଲ ଭାବରେ ବୁଝିପାରିଲ । ମାନେ ବହି କେବଳ ଓଡ଼ିଆ ଅର୍ଥ ଦେଇଥାଏ । ଏହା ଠିକ୍ ଭାବେ ଇଂରାଜୀ ଶିକ୍ଷା ପାଇଁ ଦରକାରୀ ନୁହେଁ ।

Notes And Glossary:
next ( ନେଷ୍ଟ ) – ପରେ
happened (ହାପେନ୍ସ) – ଘଟିଲା
topic (ଟପିକ୍) – ବିଷୟ/ବିଷୟବସ୍ତୁ
idea (ଆଇଡ଼ିଆ) – ଧାରଣା
silent (ସାଇଲେଣ୍ଟ୍) – ନୀରବ
facts (ଫ୍ରାକୃସ୍) – ତଥ୍ୟାବଳୀ
examples (ଏକ୍‌ଜାମ୍ପୁଲସ୍ ) – ଉଦାହରଣସମୂହ
bigger (ବିଗର୍ ) – ବୃହତ୍ତର
circle (ସର୍କଲ୍) – ବୃତ୍ତ
oval shapes (ଓଭାଲ୍ ସେପ୍‌) – ଅଣ୍ଡା ଆକୃତିର
different (ଡିଫରେଣ୍ଡ୍) – ଭିନ୍ନ/ଅଲଗା
properly (ପ୍ରପର୍‌ଲି) – ଠିକ୍ ଭାବରେ
understand ( ଅଣ୍ଡରଷ୍ଟାଣ୍ଡ୍) – ବୁଝିବା

Comprehension Questions (ବୋଧପରିମାପକ ପ୍ରଶ୍ନବଳୀ)

Question 1.
Who played the role of teacher in this paragraph?
(ଏହି ଅନୁଚ୍ଛେଦରେ କିଏ ଶିକ୍ଷକ ଭୂମିକା ନିର୍ବାହ କରିଥିଲେ ?)
Answer:
Mr. Giri played the role of teacher in this paragraph.

Question 2.
Who played the role of the student in this paragraph?
(ଏହି ଅନୁଚ୍ଛେଦରେ କିଏ ଶିକ୍ଷାର୍ଥୀ ଭୂମିକା ନିର୍ବାହ କରିଥିଲେ ? )
Answer:
Mitu played the role of the student in this paragraph.

Question 3.
How is one paragraph of a text different from another paragraph?
(ପାଠ୍ୟ ବିଷୟର ଗୋଟିଏ ଅନୁଚ୍ଛେଦ ଅନ୍ୟ ଏକ ଅନୁଚ୍ଛେଦଠାରୁ ଭିନ୍ନ କିପରି ? )
Answer:
Every paragraph has an idea or topic. In this respect two paragraphs of a text are different.

Question 4.
What does a writer do after giving the topic of the paragraph?
(ଜଣେ ଲେଖକ ବିଷୟ ସ୍ଥିର କଲାପରେ କ’ଣ କରନ୍ତି ?)
Answer:
After telling the topic, the writer gives some examples to explain the topic.

Question 5.
When Mitu answered the questions, did she keep her textbook open or closed?
(ମିତୁ ଯେତେବେଳେ ଉତ୍ତର ଦେଉଥିଲା, ସେ ପାଠ୍ୟପୁସ୍ତକ ଖୋଲା ରଖୁଥିଲା ନା ବନ୍ଦ କରିଥିଲା ?)
Answer:
When Mitu answered the questions, she kept her textbook open.

Question 6.
Was she able to answer most of the questions?
(ସେ ଅଧିକାଂଶ ପ୍ରଶ୍ନର ଉତ୍ତର ଦେବାରେ ସମର୍ଥ ହେଲା କି ?)
Answer:
Yes, she was able to answer most of the questions.

Question 7.
Is her uncle a good teacher ? How do you know?
(ତାଙ୍କର ମାମୁ ଜଣେ ଭଲ ଶିକ୍ଷକ କି ? ତୁମେ କିପରି ଜାଣୁଛ ?)
Answer:
Yes, her uncle is a good teacher. He explained the paragraph to Mitu bit by bit and made her understand everything.

Question 8.
Do you like the notes that her uncle made on the paragraph?
(ତା’ର ମାମୁ ଅନଚ୍ଛେଦ ଉପରେ ପ୍ରସ୍ତୁତ କରିଥିବା ସଂକ୍ଷିପ୍ତ ସାରାଂଶକୁ ତୁମେ ପସନ୍ଦ କରୁଛ କି ?)
Answer:
Yes, we like the notes that her uncle made on the paragraph.

Question 9.
Will the note help Mitu remember the paragraph?
(ଅନୁଚ୍ଛେଦଟିକୁ ମନେରଖ୍କୁ ମିତୁକୁ ସଂକ୍ଷିପ୍ତ ସାରାଂଶ ସାହାଯ୍ୟ କରିବ କି ?)
Answer:
Yes, the note will definitely help Mitu to remember the paragraph.

Question 10.
Why is meaning book not useful according to Mitu?
(ମିତୁ କହିବା ଅନୁସାରେ ମାନେ ବହି କାହିଁକି ଦରକାରୀ ନୁହେଁ ?)
Answer:
Meaning book is not at all useful, because it only gives the Odia meaning of the topic, but does not give knowledge.

Question 11.
What did her uncle say about meaning book?
(ତା’ର ମାମୁ ମାନେ ବହି ବିଷୟରେ କ’ଣ କହିଲେ ?)
Ans.
Her uncle said that meaning book is useless because it gives the Odia meaning only. It does not help in learning English properly.

Session – 3 (ତୃତୀୟ ପର୍ଯ୍ୟାୟ)

• SGP-3 (Sense Group Paragraph-3)
• Read paragraph-6 and 7 and answer the questions that follow.
  (ଅନୁଚ୍ଛେଦ ୬ ଓ ୭କୁ ପାଠ କର ଏବଂ ନିମ୍ନପ୍ରଦତ୍ତ ପ୍ରଶ୍ନଗୁଡ଼ିକର ଉତ୍ତର ଦିଅ ।)

6. Situ was silently sitting and watching what happened between her uncle and her sister. She broke her silence and asked, ‘If our teachers read aloud a paragraph and explain the meaning in Odia, are they doing the right thing ?”No, not at all. They are as harmful as the bazzar note”said Mr. Giri.

7. What happened after this is the story of Situ. Situ said how meaning books have lots of mistakes. One of her teachers did not give her any mark for an answer. He thought the wrong answer in the bazzar note was the right answer. She took this matter to her headmistress. She called the teacher and asked him to give her mark. She also banned the use of bazzar note books in their school. She made Situ the leader of the movement against meaning books in their school.

୬.ସିତୁ ନୀରବରେ ବସି ଲକ୍ଷ୍ୟ କରୁଥିଲା ଯାହା ତା’ର ମାମୁ ଓ ଭଉଣୀ ମଧ୍ଯରେ ଘଟୁଥିଲା । ନୀରବତା ଭାଙ୍ଗି ସେ ପଚାରିଲା, ‘‘ଯଦି ଆମେ ଶିକ୍ଷକମାନେ ଗୋଟିଏ ଅନୁଚ୍ଛେଦକୁ ବଡ଼ପାଟିରେ ପଢ଼ନ୍ତି ଏବଂ ଏହାର ଅର୍ଥ ଓଡ଼ିଆରେ ବୁଝାନ୍ତି, ସେମାନେ କ’ଣ ଠିକ୍ କରନ୍ତି ?’’ କେବେ ନୁହେଁ ! ଗିରିବାବୁ କହିଲେ, ‘ସେମାନେ ବଜାରର ମାନେ ବହି ପରି କ୍ଷତିକାରକ ଅଟନ୍ତି ।’’

୭.ଏହାପରେ ଯାହା ଘଟିଲା ତାହା ସିତୁର କାହାଣୀ ଥିଲା । ସିତୁ କହିଲା କିପରି ମାନେବହିଗୁଡିକରେ ବହୁତ ଭୁଲ ବା ତ୍ରୁଟି ରହୁଛି । ତା’ର ଜଣେ ଶିକ୍ଷକ ଗୋଟିଏ ପ୍ରଶ୍ନର ଉତ୍ତର ପାଇଁ ତାକୁ କିଛି ନମ୍ବର ଦେଇ ନଥିଲେ । ସେ ବଜାର ମାନେ ବହିରେ ଥିବା ଭୁଲ ଉତ୍ତରକୁ ଠିକ୍ ଉତ୍ତର ବୋଲି ଭାବୁଥିଲେ । ସେ (ସିତୁ) ଏହି ଘଟଣାକୁ ପ୍ରଧାନ ଶିକ୍ଷୟିତ୍ରୀଙ୍କ ଦୃଷ୍ଟିକୁ ଆଣିଲେ । ସେ ଶିକ୍ଷକକୁ ଡାକିଲେ ଏବଂ କହିଲେ ତାକୁ ନମ୍ବର ଦେବାକୁ । ସେ ମଧ୍ୟ ବଜାର ମାନେ ବହିଗୁଡିକୁ ତାଙ୍କ ବିଦ୍ୟାଳୟରେ ବ୍ୟବହାର କରିବାକୁ ନିଷେଧ କଲେ । ସେ ତାଙ୍କ ବିଦ୍ୟାଳୟରେ ବଜାର ମାନେ ବହି ବିରୋଧୀ ଆନ୍ଦୋଳନର ସିତୁକୁ ନେତ୍ରୀ କରିଦେଲେ ।

Notes And Glossary: (ଶବ୍ଦାର୍ଥ) :
watching (ଚିଙ୍ଗ୍) – ଦେଖିବା
broke (ବ୍ରୋକ୍) – ଭାଙ୍ଗିଲା
silence (ସାଇଲେନ୍ସ) – ନୀରବତା
not at all (ନଟ୍ ଆଟ୍ ଅଲ୍) – ଆଦୌ ନୁହେଁ
harmful (ହାର୍ମଫୁଲ୍) – କ୍ଷତିକାରକ
bazzar (ବଜାର)
banned – ନିଷେଧ କଲେ

Comprehension Questions (ବୋଧପରିମାପକ ପ୍ରଶ୍ନବଳୀ) :
Question 1.
What are these two paragraphs about-about Mitu, Mr. Giri or Situ ?
(ଏହି ଦୁଇଟି ଅନୁଚ୍ଛେଦ କାହା ବିଷୟରେ – ମିତ୍ରୁ, ମି.ଗିରି ନା ସିତୁ ବିଷୟରେ ?)
Answer:
These two paragraphs are about Situ.

Question 2.
Who said meaning books have lots of mistakes ?
(ମାନେ ବହିରେ ଅନେକ ଭୁଲ୍ ଅଛି ବୋଲି କିଏ କହିଥିଲା ?)
Answer:
Situ said that the meaning books have lots of mistakes.

Question 3.
Even if the answer of Situ was correct, why didn’t her teacher give her any mark?
(ଯଦିଓ ସିତୁର ଉତ୍ତର ଠିକ୍ ଥିଲା, ତା’ର ଶିକ୍ଷକ ତାକୁ କାହିଁକି କୌଣସି ନମ୍ବର ଦେଲେ ନାହିଁ ।)
Answer:
Though the answer of Situ was correct, her teacher didn’t give her any mark, because he thought that the wrong answer in the bazzar note was the right answer.

Question 4.
What did Situ do next?
(ତା’ପରେ ସିତୁ କ’ଣ କଲା ?)
Answer:
Then Situ took the matter to her headmistress.

Question 5.
What did the headmistress ban?
(ପ୍ରଧାନ ଶିକ୍ଷୟିତ୍ରୀ କ’ଣ ନିଷେଧ କରିଥିଲେ ?)
Answer:
The headmistress banned the use of bazzar note books in their school. She also made Situ the leader of the movement against bazzar note books in their school.

Question 6.
What was the movement about?
(ଆନ୍ଦୋଳନ କେଉଁ ବିଷୟରେ ଥିଲା ? )
Answer:
The movement was against the use of meaning books in their school.

Question 7.
Who did the headmistress make the leader of the movement? Why?
(ପ୍ରଧାନ ଶିକ୍ଷୟିତ୍ରୀ କାହାକୁ ଆନ୍ଦୋଳନର ନେତ୍ରୀ କରାଇଲେ ? କାହିଁକି ?)
Answer:
The headmistress made Situ the leader of the movement. Because Situ knew well about the harmful impact of the bazzar note books.

Question 8.
Will you use meaning book after reading this lesson?
(ଅଧ୍ୟାୟ ପଢ଼ି ସାରିବା ପରେ ତୁମେମାନେ ମାନେବହି ବ୍ୟବହାର କରିବ କି ?)
Answer:
No, we will never use the meaning books after reading this les son.

Session – 4 (ଚତୁର୍ଥ ପର୍ୟ୍ୟାୟ)
Post-Reading (ପଠନ ପରବର୍ତ୍ତୀ)

1. Visual Memory Development Technique (VMDT) :
(ଦୃଶ୍ୟ ସ୍ମୃତି ବିଚାର କୌଶଳ) : (Teacher decides)

2. Comprehension Activities (ବୋଧ ପରିମାପକ କାର୍ଯ୍ୟାବଳୀ) :
(a) Teacher frames MCQs. (ଶିକ୍ଷକ MCQ ତିଆରି କରନ୍ତୁ)
(b) The lesson is divided into three SGPs : three parts. The three topics/themes are given.
Write under each paragraph number. (Question with Answer)

3. Listening (ଶୁଣିବା) :
Teacher frames listening activities.

Session – 5 (ଷଷ୍ଠ ପର୍ଯ୍ୟାୟ)
4. Speaking (କଥନ) :

(a) Chain-drill: Meaning books are harmful.
(b) Dialogue: (Follow the steps of previous lessons.)
Mr Giri: Where is Melbourne?
Mitu: In Australia
Mr Giri: Where is Feroz Shah Kotla Cricket Ground?
Mitu: In New Delhi
Mr Giri: Where is Chepauk Ground?
Mitu: In Chennai

5. Vocabulary ଶବ୍ଦାବଳୀ:
Match the words with the shapes. (Question with Answer)

6. Writing (ଲିଖନାତ୍ମକ)

(a) Teacher gives some questions for writing in one sentence each.
(b) See the notes given by Mr. Giri on the paragraph. Now write a paragraph based on the notes. (Do not see the original paragraph while doing this task). Some help is given.

The paragraph is about __________ cricket ground. __________. Some cricket grounds are_____________. Some are ___________. The Melbourne ____________is ___________than the ___________. Some __________ are circular. Some ____________ are _________. The ___________ is ___________. The ___________is oval. The Melbourne _____________is in Australia.
Answer:
The paragraph is about size and shape of cricket ground. Some cricket grounds are bigger. Some are smaller. The Melbourne cricket ground is bigger than the Feroz Shah. Some cricket ground are circular. Some cricket grounds are oval. The Chepauk cricket ground is circular. The Adelaide cricket ground is oval. The Melbourne cricket ground is in Australia.

7. Mental Talk (ମାନସ କଥନ) :

_____________________________________________________

_____________________________________________________.
8. Let’s Think (ଚାଲ ଚିନ୍ତା କରିବା ବା କଳ୍ପନା କରିବା):

_____________________________________________________

_____________________________________________________.

Word Note: (The words/phrases have been defined mostly on their contextual meanings)

acute (ଆକ୍ୟୁଟ୍) – intense, severe (ଉତ୍କଟ)
ban – to say that something must not be done
bull dog (ବୁଲ୍ ଡର)- a type of strong dog (ଏକ ପ୍ରକାର ଶକ୍ତିଶାଳୀ କୁକୁର)
Chinese Great Wall (ଚାଇନିଜ୍ ଗ୍ରେଟ୍ ୱାଲ୍) – Historic Great Wall of Chine (ପ୍ରାଚୀର)
dazzling (ଡାକ୍‌ଲିଙ୍ଗ୍) – very bright (ଚମକୁଥୁବା )
disappear (ଡିସ୍‌ପିୟର) – to go away (ଅଦୃଶ୍ୟ ହେବା । ଦୂର ହେବା)
disturbed (ଡିଷ୍ଟର୍ବଡ୍) – made him worried/unhappy  (କଲା)
encyclopedias (ଏନସାଇକ୍ଲୋପିଡିଆ) – knowledge books (ଜ୍ଞାନ ପୁସ୍ତକ)
flooded (ଫ୍ଲଡେଡ୍) – filled with (moon light) (ଚନ୍ଦ୍ର ଆଲୋକ) ରେ ପରିପୂର୍ଣ୍ଣ
glamour (ଗ୍ଲାମର୍) – beauty (ସୌନ୍ଦର୍ଯ୍ୟ)
in contrast (ଇନ୍ କନ୍‌ଷ୍ଟ୍ରିଟ୍) – in comparison (ତୁଳନାତ୍ମକ ଭାବରେ)
indifferent (ଇନ୍‌ଫରେଣ୍ଡ୍) – lack of interest (ଅନାଗ୍ରହ)
lit by lamps (ପ୍ରଦୀପ ଦ୍ୱାରା ପ୍ରଜ୍ୱଳିତ) – lighted with lamps
palatial building (ପାଲଟିଆ ବିଲଡିଂ) – royal building (ରାଜକୀୟ ଭବନ)
prison (ପ୍ରିଜନ୍) – a building where usually thieves and criminals are kept for punishment
privileged (ପ୍ରିଭିଲିଜ୍) – blest with special benefits, wealth etc. (ବିଶେଷ ଅଧିକାରପ୍ରାପ୍ତ)
richness (ରିନେସ୍ ) – the quality of being rich (ବିତ୍ତଶାଳୀ ଭାବ)
sadness (ସ୍ୟାଡ଼ନେସ୍ ) – unhappiness (ଦୁଃଖ | ବିଷାଦ)
scattered (ସ୍କାଟର୍‌ଡ଼) – seen over a wide area (ବିଛୁରିତ)
surrounded (ସରାଉଣ୍ଡେଡ୍) – covered from all sides
tiny – small (ଛୋଟ)
toiling (ଟଏଲିଙ୍ଗ୍) – doing hard labour (ଅତ୍ୟଧ୍ଵ ପରିଶ୍ରମ କରୁଥିବା)
wretched condition – very poor condition
similarity (ସିମିଲାରିଟି) – ସମାନତା
warrior (ୱାରିଅର୍) – soldier (ଯୋଦ୍ଧା, କିନ୍ତୁ ଏଠାରେ ଭୁଲ ବ୍ୟବସ୍ଥା ବିରୁଦ୍ଧରେ ଲଢ଼ୁଥିବା ବ୍ୟକ୍ତି ପାଇଁ ବ୍ୟବହାର କରାଯାଇଛି)।

BSE Odisha 7th Class English Solutions Follow-Up Lesson 2 A Tiny Warrior Important Questions and Answers

(A) Choose the right answer from the options.
Question 1.
Mitu studies in class VII but Situ studies in class __________.
(i) IX
(iii) IV
(iv) V
(ii) X
Answer:
(iv) V

Question 2.
Mr. giri was their _________.
(i) uncle
(ii) father
(iii) grandfather
(iv) brother
Answer:
(i) uncle

Question 3.
The Melbourne cricket ground is in ___________.
(i) America
(ii) Japan
(iii) Australia
(iv) Korea
Answer:
(iii) Australia

Question 4.
Situ’s answer was correct but the teacher didn’t give her any mark because he ___.
(i) her handwriting is not good
(ii) she copied it from another student
(iii) he thought wrong answer of bazzar notebok to be correct
(iv) his relation with Mitu is not good.
Answer:
(iii) he thought wrong answer of bazzar notebok to be correct

Question 5.
The headmistress made __________the leader of the movement against meaning books in their school.
(i) Situ
(ii) Mitu
(iii) Mr. Giri
(iv) the English teacher
Answer:
(i) Situ

(B) Answer the following questions.
Question 1.
Are bazzar note books useful for students? Why? or Why not?
Answer:
No, the bazzar note books are not useful for students. They have lot of mistakes and a student can’t learn English properly by using them.

Question 2.
Why did Mr. Giri want to help Mitu in learning English?
Answer:
Mr. Giri saw Mitu reading a paragraph of English lesson from textbook and then followed a bazzar note book for its meaning. As this would not help her in learning English properly, so he wanted to help her.

(C) Re-arrange the jumbled words to make meaningful sentences.
1. attacks / the / his / walls / were / protection / outside / from
Answer:
The walls were his protection from outside attacks.

2. the / in / nights/building / moonlit / looked / beautiful / very
Answer:
In moonlit nights, the building looked very beautiful.

3. man / the / lived / rich /, / there / a / like / king / happily / very
Answer:
The rich man lived there like a king very happily.

4. people / to / poor / the / one / the / day/man / rich / his / took / son
Answer:
One day the rich man took his son to the poor people.

5. food / they /, / theirs / buy / me / grow
Answer:
We buy food, they grow theirs.

(D) Find whether True or False.
1. Once upon a time there was a very rich man.
Answer:
True

2. He along with his family lived in a small hut down the hill.
Answer:
False

3. The building, the walls all around and the gardens inside were lit by moonlight.
Answer:
False

4. His only sorrow was that his Only son did not like all his richness and glamour.
Answer:
True

5. One day the rich man took his son to wander in the forest.
Answer:
False

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Additional Exercise Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Additional Exercise

(A) Multiple Choice Questions (Mcqs) With Answers

Question 1.
Write the value of cos^-1 cos(3π/2).
(a) π
(b) \(\frac{\pi}{2}\)
(c) \(\frac{\pi}{4}\)
(d) 2π
Solution:
(b) \(\frac{\pi}{2}\)

Question 2.
Sets A and B have respectively m and n elements. The total number of relations from A to B is 64. If m < n and m ≠ 1, write the values of m and n respectively.
(a) m = 3, n = 2
(b) m = 2, n = 2
(c) m = 2, n = 3
(d) m = 3, n = 3
Solution:
(c) m = 2, n = 3

Question 3.
Write the principal value of
sin^-1 (\(-\frac{1}{2}\)) + cos^-1 cos(\( -\frac{\pi}{2}\))
(a) \(\frac{\pi}{2}\)
(b) \(\frac{\pi}{3}\)
(c) \(\frac{\pi}{4}\)
(d) π
Solution:
(b) \(\frac{\pi}{3}\)

Question 4.
Write the maximum value of x + y subject to: 2x + 3y < 6, x > 0, y > 0.
(a) 3
(b) 1
(c) 2
(d) 0
Solution:
(a) 3

Question 5.
Let A has 3 elements and B has m elements. Number of relations from A to B = 4096. Find the value of m.
(a) 2
(b) 4
(c) 1
(d) 3
Solution:
(b) 4

Question 6.
Let A is any non-empty set. Number of binary operations on A is 16. Find |A|.
(a) 2
(b) 1
(c) 3
(d) 4
Solution:
(a) 2

Question 7.
Give an example of a relation which is reflexive, transitive but not symmetric.
(a) x < y on Z
(b) x = y on Z
(c) x > y on Z
(d) None of the above
Solution:
(a) x < y on Z

Question 8.
Find the least positive integer r such that – 375 ∈ [r]₁₁
(a) r = 5
(b) r = 6
(c) r = 3
(d) r = 10
Solution:
(d) r = 10

Question 9.
Find three positive integers x_i, i = 1, 2, 3 satisfying 3x ≡ 2 (mod 7)
(a) x = 1, 3, 9…
(b) x = 2, 4, 6…
(c) x = 3, 10, 17…
(d) x = 2, 10, 18…
Solution:
(c) x = 3, 10, 17…

Question 10.
If the inversible function f is defined as f(x) = \(\frac{3 x-4}{5}\) write f^-1(x)
(a) \(\frac{5 x+4}{3}\)
(b) \(\frac{4 x+5}{3}\)
(c) \(\frac{5 x-4}{3}\)
(d) \(\frac{5 x+4}{2}\)
Solution:
(a) \(\frac{5 x+4}{3}\)

Question 11.
Let f : R → R and g : R → R defined as f(x) = |x|, g(x) = |5x – 2| then find fog.
(a) |5x + 2|
(b) |5x – 2|
(c) |2x – 2|
(d) |2x – 5|
Solution:
(b) |5x – 2|

Question 12.
Let ∗ is a binary operation defined by a ∗ b = 3a + 4b – 2, find 4 ∗ 5.
(a) 20
(b) 12
(c) 30
(d) 36
Solution:
(c) 30

Question 13.
Let the binary operation on Q defined as a ∗ b = 2a + b – ab, find 3 ∗ 4.
(a) -2
(b) -1
(c) 2
(d) 1
Solution:
(a) -2

Question 14.
Let ∗ is a binary operation on Z defined as a ∗ b = a + b – 5 find the identity element for ∗ on Z.
(a) e = 1
(b) e = 5
(c) e = -5
(d) e = -1
Solution:
(b) e = 5

Question 15.
Find the number of binary, operations on the set {a, b}.
(a) 12
(b) 14
(c) 15
(d) 16
Solution:
(d) 16

Question 16.
Let ∗ is a binary operation on [0, ¥) defined as a ∗ b = \(\sqrt{a^2+b^2}\) find the identity element.
(a) e = 0
(b) e = 2
(c) e = 1
(d) e = 3
Solution:
(a) e = 0

Question 17.
Find least non-negative integer r such that 7 × 13 × 23 × 413 ≡ r (mod 11).
(a) r = 13
(b) r = 49
(c) r = 7
(d) r = 23
Solution:
(c) r = 7

Question 18.
Find least non-negative integer r such that 1237(mod 4) + 985 (mod 4) ≡ r (mod 4).
(a) r = 1
(b) r = 2
(c) r = -2
(d) r = -1
Solution:
(b) r = 2

Question 19.
Let ∗ is a binary operation on R – {0} defined as a ∗ b = \(\frac{a b}{5}\). If 2 ∗ (x ∗ 5) = 10, then find x:
(a) x = 25
(b) x = -5
(c) x = 5
(d) x = 1
Solution:
(a) x = 25

Question 20.
Find the principal value of cos^-1 (\( -\frac{1}{2}\)) + 2sin^-1 (\( \frac{1}{2}\)).
(a) \(\frac{5 \pi}{6}\)
(b) \(\frac{5 \pi}{2}\)
(c) \(\frac{5 \pi}{4}\)
(d) \(\frac{\pi}{6}\)
Solution:
(a) \(\frac{5 \pi}{6}\)

Question 21.
Evaluate sin^-1 (\(\frac{1}{\sqrt{5}}\)) + cos^-1 (\(\frac{3}{\sqrt{10}}\))
(a) \(\frac{\pi}{2}\)
(b) \(\frac{\pi}{5}\)
(c) \(\frac{\pi}{4}\)
(d) π
Solution:
(c) \(\frac{\pi}{4}\)

Question 22.
Evaluate cos^-1 (\(\frac{1}{2}\)) + 2sin^-1 (\(\frac{1}{2}\)).
(a) \(\frac{2 \pi}{5}\)
(b) \(\frac{2 \pi}{3}\)
(c) π
(d) \(\frac{\pi}{3}\)
Solution:
(b) \(\frac{2 \pi}{3}\)

Question 23.
Find the value of tan^-1 √3 – sec^-1 (-2).
(a) –\(\frac{\pi}{3}\)
(b) \(\frac{2 \pi}{3}\)
(c) \(\frac{\pi}{3}\)
(d) \(\frac{3 \pi}{2}\)
Solution:
(a) –\(\frac{\pi}{3}\)

Question 24.
Evaluate tan (2 tan^-1 \(\frac{1}{3}\))
(a) 2
(b) 1
(c) 0
(d) -1
Solution:
(a) 2

Question 25.
Evaluate : sin^-1 (sin \(\frac{3 \pi}{5}\)).
(a) \(-\frac{2 \pi}{3}\)
(b) \(\frac{\pi}{3}\)
(c) \(\frac{2 \pi}{5}\)
(d) \(\frac{\pi}{5}\)
Solution:
(c) \(\frac{2 \pi}{5}\)

Question 26.
tan^-1 (2cos\(\frac{\pi}{3}\)) is ________.
(a) \(\frac{\pi}{2}\)
(b) \(\frac{\pi}{4}\)
(c) \(\frac{\pi}{5}\)
(d) \(\frac{\pi}{3}\)
Solution:
(b) \(\frac{\pi}{4}\)

Question 27.
Evaluate : sin^-1 (sin \(\frac{2 \pi}{3}\)) is ________.
(a) \(\frac{\pi}{2}\)
(b) \(\frac{\pi}{4}\)
(c) \(\frac{\pi}{5}\)
(d) \(\frac{\pi}{3}\)
Solution:
(d) \(\frac{\pi}{3}\)

Question 28.
The value of sin(tan^-1 x + tan^-1 \( \frac{1}{x}\)), x > 0 = ________.
(a) -1
(b) 1
(c) 0
(d) 2
Solution:
(b) 1

Question 29.
2sin^-1 \( \frac{4}{5}\) + sin^-1 \( \frac{24}{25}\) = ________.
(a) 12
(b) 15
(c) 16
(d) 20
Solution:
(b) 15

Question 30.
Evaluate: tan^-1 1 = (2cos\(\frac{\pi}{3}\))
(a) \(\frac{\pi}{4}\)
(b) \(\frac{\pi}{2}\)
(c) \(\frac{\pi}{3}\)
(d) \(\frac{2 \pi}{3}\)
Solution:
(a) \(\frac{\pi}{4}\)

Question 31.
If sin^-1 (\( \frac{\pi}{5}\)) + cosec^-1 (\(\frac{5}{4}\)) = \(\frac{5}{2}\) then find the value of x.
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
(c) 3

Question 32.
Evaluate:
tan^-1 (\( \frac{-1}{\sqrt{3}}\)) + cot^-1 (\( \frac{1}{\sqrt{3}}\)) + tan^-1(sin(\( -\frac{\pi}{2}\))).
(a) \(\frac{- \pi}{12}\)
(b) \(\frac{2 \pi}{5}\)
(c) \(\frac{\pi}{12}\)
(d) \(\frac{\pi}{6}\)
Solution:
(a) \(\frac{- \pi}{12}\)

Question 33.
Evaluate sin^-1 (cos(\( \frac{33 \pi}{5}\)))
(a) \(\frac{\pi}{10}\)
(b) \(\frac{- \pi}{10}\)
(c) \(\frac{\pi}{5}\)
(d) \(\frac{\pi}{2}\)
Solution:
(b) \(\frac{- \pi}{10}\)

Question 34.
Express the value of the following in simplest form. tan (\( \frac{\pi}{4}\) + 2cot^-1 3)
(a) 7
(b) 12
(c) 3
(d) 6
Solution:
(a) 7

Question 35.
Express the value of the following in simplest form sin cos^-1 tan sec^-1 √2
(a) cos 0
(b) cot 0
(c) tan 0
(d) sin 0
Solution:
(d) sin 0

Question 36.
tan \(\left\{\frac{1}{2} \sin ^{-1} \frac{2 x}{1+x^2}+\frac{1}{2} \cos ^{-1} \frac{1-y^2}{1+y^2}\right\}\)
(a) \(\frac{x-y}{1+x y}\)
(b) \(\frac{x+y}{1-x y}\)
(c) \(\frac{x-y}{1+y}\)
(d) \(\frac{x+y}{x y}\)
Solution:
(b) \(\frac{x+y}{1-x y}\)

Question 37.
The relation R on the set A = [1, 2, 3] given by R = {(1, 1), (1, 2), (2, 2), (2, 3), (3, 3)} is:
(a) Reflexive
(b) Symmetric
(c) Transitive
(d) Equivalence
Solution:
(a) Reflexive

Question 38.
Let f : R → R be defined as f(x) = 3x – 2. Choose the correct answer.
(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto
Solution:
(a) f is one-one onto

Question 39.
Let R be a relation defined on Z as R = {(a, b) ; a² + b² = 25 }, the domain of R is:
(a) {3, 4, 5}
(b) {0, 3, 4, 5}
(c) {0, 3, 4, 5, -3, -4, -5}
(d) None of the above
Solution:
(c) {0, 3, 4, 5, -3, -4, -5}

Question 40.
let R be the relation in the set N given by R={(a, b) : a = b – 2, b > 6}. Choose the correct answer.
(a) (2, 4) • R
(b) (3, 8) • R
(c) (6, 8) • R
(d) (8, 10) • R
Solution:
(d) (8, 10) • R

Question 41.
Set A has 3 elements and set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is
(a) 144
(b) 12
(c) 24
(d) 64
Solution:
(c) 24

Question 42.
Let R be a relation on set of lines as L₁ R L₂ if L₁ is perpendicular to L₂. Then
(a) R is Reflexive
(b) R is transitive
(c) R is symmetric
(d) R is an equivalence relation
Solution:
(c) R is symmetric

Question 43.
A Relation from A to B is an arbitrary subset of:
(a) A × B
(b) B × B
(c) A × A
(d) B × B
Solution:
(a) A × B

Question 44.
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is
(a) reflexive but not transitive
(b) transitive but not symmetric
(c) equivalence
(d) None of these
Solution:
(c) equivalence

Question 45.
The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5
Solution:
(d) 5

Question 46.
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
(a) reflexive but not symmetric
(b) reflexive but not transitive
(c) symmetric and transitive
(d) neither symmetric nor transitive
Solution:
(a) reflexive but not symmetric

Question 47.
Which of the following functions from Z into Z are bijective?
f(x) = x³
f(x) = x + 2
f(x) = 2x + 1
f(x) = x² + 1
Solution:
f(x) = x + 2

Question 48.
Let R be a relation on the set N of natural numbers denoted by nRm <=> n is a factor of m (i.e. n | m). Then, R is
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric
Solution:
(c) Equivalence

Question 49.
Let S = {1, 2, 3, 4, 5} and let A = S × S. Define the relation R on A as follows: (a, b) R (c, d) iff ad = cb. Then, R is
(a) reflexive only
(b) Symmetric only
(c) Transitive only
(d) Equivalence relation
Solution:
(d) Equivalence relation

Question 50.
Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defined by y = 2x⁴, is
(a) one-one onto
(b) one-one into
(c) many-one onto
(d)many-one into
Solution:
(c) many-one onto

Question 51.
Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x) = (x-2)/(x-3). Then,
(a) f is bijective
(b) f is one-one but not onto
(c) f is onto but not one-one
(d) None of these
Solution:
(a) f is bijective

Question 52.
The function f : R → R given by f(x) = x³ – 1 is
(a) a one-one function
(b) an onto function
(c) a bijection
(d) neither one-one nor onto
Solution:
(c) a bijection

Question 53.
Let f : [0, ∞) → [0, 2] be defined by f(x) = 2x/1+x, then f is
(a) one-one but not onto
(b) onto but not one-one
(c) both one-one and onto
(d) neither one-one nor onto
Solution:
(a) one-one but not onto

Question 54.
If N be the set of all natural numbers, consider f : N → N such that f(x) = 2x, ∀ × ∈ N, then f is
(a) one-one onto
(b) one-one into
(c) many-one onto
(d) None of these
Solution:
(b) one-one into

Question 55.
Let f : R → R be a function defined by f(x) = x³ + 4, then f is
(a) injective
(b) surjective
(c) bijective
(d) none of these
Solution:
(c) bijective

Question 56.
Given set A = {a, b, c}. An identity relation in set A is
(a) R = {(a, b), (a, c)}
(b) R = {(a, a), (b, b), (c, c)}
(c) R = {(a, a), (b, b), (c, c), (a, c)}
(d) R= {(c, a), (b, a), (a, a)}
Solution:
(b) R = {(a, a), (b, b), (c, c)}

Question 57.
Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is
(a) 144
(b) 12
(c) 24
(d) 64
Solution:
(c) 24

Question 58.
sin(sec^-1 x + cosec^-1 x) =
(a) 1
(b) -1
(c) π/2
(d) π/3
Solution:
(a) 1

Question 59.
The principle value of sin^-1 (√3/2) is:
(a) 2π/3
(b) π/6
(C) π/4
(d) π/3
Solution:
(d) π/3

Question 60.
Simplified form of cos^-1 (4x³ – 3x)
(a) 3 sin^-1 x
(b) 3 cos^-1 x
(c) π – 3 sin^-1 x
(d) None of these
Solution:
(b) 3 cos^-1 x

Question 61.
tan^-1 √3 – sec^-1 (-2) is equal to
(a) π
(b) -π/3
(c) π/3,
(d) 2π/3
Solution:
(b) -π/3

Question 62.
If y = sec^-1 x then
(a) 0 ≤ y ≤ π
(b) 0 ≤ y ≤ π/2
(c) -π/2 ≤ y ≤ π/2
(d) None of these
Solution:
(d) None of these

Question 63.
If x + (1/x) = 2 then the principal value of sin^-1 x is
(a) π/4
(b) π/2
(c) π
(d) 3π/2
Solution:
(b) π/2

Question 64.
The principle value of sin^-1 (sin 2π/3) is :
(a) 2π/3
(b) π/3
(c) -π/6
(d) π/6
Solution:
(b) π/3

Question 65.
The value of cos^-1 (1/2) + 2sin^-1 (1/2) is equal to
(a) π/4
(b) π/6
(c) 2π/3
(d) 5π/6
Solution:
(b) π/6

Question 66.
Principal value of tan^-1 (-1) is
(a) π/4
(b) -π/2
(c) 5π/4
(d) -π/4
Solution:
(d) -π/4

Question 67.
A Linear function, which is minimized or maximized is called
(a) an objective function
(b) an optimal function
(c) A feasible function
(d) None of these
Solution:
(a) an objective function

Question 68.
The maximum value of Z = 3x + 4y subject to the constraints : x+ y ≤ 4, x ≥ 0, y ≥ 0 is:
(a) 0
(b) 12
(c) 16
(d) 18
Solution:
(c) 16

Question 69.
The maximum value of Z = 2x +3y subject to the constraints : x + y ≤ 1, 3x + y ≤ 4, x, y ≥ 0 is
(a) 2
(b) 4
(c) 5
(d) 3
Solution:
(c) 5

Question 70.
The point in the half plane 2x + 3y – 12 ≥ 0 is:
(a) (-7,8)
(c) (-7,-8)
(b) (7, -8)
(d) (7, 8)
Solution:
(d) (7, 8)

Question 71.
Any feasible solution which maximizes or minimizes the objective function is Called:
(a) A regional feasible solution
(b) An optimal feasible solution
(c) An objective feasible solution
(d) None of these
Solution:
(b) An optimal feasible solution

Question 72.
Objective function of a LPP is
(a) a constraint
(b) a function to be optimized
(c) a relation between the variables
(d) none of these
Solution:
(b) a function to be optimized

(B) Very Short Type Questions With Answers

Question 1.
If R is a relation on A such that R = R^-1, then write the type of the relation R.
Solution:
We know that (a, b) ∈ R ⇒ (b, a) ∈ R^-1
As R = R^-1, so R is symmetric. [2019(A)

Question 2.
Write the value of cos^-1 cos (\(\frac{3 \pi}{2}\)). [2019(A)
Solution:
cos^-1 cos (\(\frac{3 \pi}{2}\)) = cos^-1 (0) = \(\frac{\pi}{2}\)

Question 3.
Sets A and B have respectively m and n elements. The total number of relations from A to B is 64. If m < n and m ≠ 1, write the values of m and n respectively. [2018(A)
Solution:
|A| = m and |B| = n
Number of relations from A to B = 2^mn.
A.T.Q. 2^mn = 64 = 2⁶.
⇒ mn = 6, m < n with m ≠ 1.
∴m = 2, n = 3

Question 4.
Write the principal value of sin^-1 (\(\frac{- 1}{2}\)) + cos^-1 cos(\(\frac{- \pi}{2}\)) [2018(A)
Solution:
sin^-1 (\(\frac{- 1}{2}\)) + cos^-1 (cos\(\frac{- \pi}{2}\)) = \(\frac{- \pi}{6}\) + \(\frac{\pi}{2}\) = \(-\frac{\pi}{3}\)

Question 5.
Write the maximum value of x + y subject to: 2x + 3y ≤ 6, x ≥ 0, y ≥ 0. [2011(A)
Solution:
2x + 3y = 6 intersects the axes at (3, 0) and (0, 2)
∴ The maximum value of x + y = 3.

Question 6.
Define ‘feasible’ solution of an LPP. [2009(A)
Solution:
The solutions of LPP which satisfy all the constraints and non-negative restrictions are called feasible solutions.

Question 7.
Mention the quadrant in which the solution of an LPP with two decision variables lies when the graphical method is adopted. [2008(A)
Solution:
The solution lies in XOY or 1st quadrant.

Question 8.
Write the smallest equivalence relation on A = {1, 2, 3}.
Solution:
The relation R = {(1, 1), (2, 2), (3, 3)} is the smallest equivalence relation on set A.

Question 9.
Congruence modulo 3 relation partitions the set Z into how many equivalence classes?
Solution:
The relation congruence modulo 3 on the set Z partitions Z into three equivalence classes.

Question 10.
Give an example of a relation which is reflexive, symmetric but not transitive.
Solution:
The relation R = {(a, b), (b, a), (a, c), (c, a), (a, a), (b, b), (c, c)} defined on the set {a, b, c} is reflexive, symmetric but not transitive.

Question 11.
Give an example of a relation which is reflexive, transitive but not symmetric.
Solution:
‘‘The relation x ≤ y on Z” is reflexive, transitive but not symmetric.

Question 12.
Give an example of a relation which is reflexive but neither symmetric nor transitive.
Solution:
The relation R = {(a, a), (b, b), (c, c), (a, b), (b, c)} defined on the set A = {a, b, c} is reflexive but neither symmetric nor transitive.

Question 13.
Find three positive integers x_i, i =1, 2, 3 satisfying 3x ≡ 2 (mod 7)
Solution:
3x ≡ 2 mod 7
Least positive value of x = 3
Each member of [3] is a solution
∴ x = 3, 10, 17…

Question 14.
State the reason for relation R on {1, 2, 3} defined as {(1, 2), (2, 1)} is not transitive.
Solution:
(1, 2), (2, 1) ∈ R but (1, 1) ∉ R
∴ R is not transitive.

Question 15.
Give an example of a function which is injective but not surjective.
Solution:
f(x) = \(\frac{x}{2}\) from Z → R is injective but not surjective.

Question 16.
Let X = {1, 2, 3, 4}. Determine whether
f : X → X defined as given below have inverses. Find f^-1 if it exists:
f = {(1, 2), (2, 2), (3, 2), (4, 2)}
Solution:
f is not injective hence not invertible.

Question 17.
Let ∗ is a binary operation defined by a ∗ b = 3a + 4b – 2, find 4 ∗ 5.
Solution:
4 ∗ 5 = 3 × 4 + 4 × 5 – 2
= 12 + 20 – 2
= 30

Question 18.
Let the binary operation on Q defined as a ∗ b = 2a + b – ab, find 3 ∗ 4.
Solution:
3 ∗ 4 = 6 + 4 – 12 = -2

Question 19.
Let ∗ is a binary operation on Z defined as a ∗ b = a + b – 5 find the identity element for ∗ on Z.
Solution:
Let e is the identity element.
⇒ a ∗ e = e ∗ a = a
⇒ a + e – 5 = a
⇒ e = 5

Question 20.
Find the number of binary operations on the set {a, b}.
Solution:
Number of binary operations on
{a, b} = 2²² = e⁴ =16.

Question 21.
Let * is a binary operation on [0, ¥) defined as a * b = \(\sqrt{\mathbf{a}^2+\mathbf{b}^2}\) find the identity element.
Solution:
Let e is the identity element
⇒ a * e = \(\sqrt{\mathbf{a}^2+\mathbf{e}^2}\) = a
⇒ a² + e² = a²
⇒ e = 0

Question 22.
Evaluate cos^-1 (\(\frac{1}{2}\)) + 2 sin^-1 (\(\frac{1}{2}\)).
Solution:
cos^-1 (\(\frac{1}{2}\)) + 2 sin^-1 (\(\frac{1}{2}\))
= \(\frac{\pi}{3}\) + 2 × \(\frac{\pi}{6}\) = \(\frac{2 \pi}{3}\)

Question 23.
Find the value of tan^-1 √3 – sec^-1 (-2)
Solution:
tan^-1 √3 – sec^-1 (-2)
= \(\frac{\pi}{3}\) – \(\frac{2 \pi}{3}\) = – \(\frac{\pi}{3}\).

Question 24.
Evaluate tan (2  tan^-1 \(\frac{1}{3}\))
Solution:
tan (2  tan^-1 \(\frac{1}{3}\)) = tan tan^-1 \(\left(\frac{\frac{2}{3}}{1-\frac{2}{3}}\right)\)
= tan tan^-1 (2) = 2

Question 25.
Evaluate: sin^-1 (sin \(\frac{3 \pi}{5}\)).
Solution:
sin^-1 (sin \(\frac{3 \pi}{5}\)) = sin^-1 sin (\(\pi \frac{-2 \pi}{5}\))
= sin^-1 sin \(\frac{2 \pi}{5}\) = \(\frac{2 \pi}{5}\)

Question 26.
Evaluate tan^-1 1 = (2 cos \(\frac{\pi}{3}\))
Solution:
tan^-1 (2 cos \(\frac{\pi}{3}\))
= tan^-1 (2 × 1/2) = tan^-1 1 = \(\frac{\pi}{4}\)

Question 27.
Define the objective function.
Solution:
If C₁, C₂, C₃ …. Cn are constants and x₁, x₂, …… x_n are variables then the linear function z = C₁x₁ + C₂x₂ +…… C_nx_n which is to be optimized is called an objective function.

Question 28.
Define feasible solution.
Solution:
A set of values of the variables x₁, x₂, …… x_n is called a feasible solution of LPP if it satisfies the constraints and non-negative restrictions of the problem.

Question 29.
Define a convex set.
Solution:
A set is convex if every point on the line segment joining any two points lies on it.

Question 30.
State extreme point theorem.
Solution:
Let S is a convex polygon bounded by the straight lines. The linear function z = Ax + By attains its optimum value at the vertices of S.

(C) Short Type Questions With Answers

Question 1.
Construct the multiplication table X₇ on the set {1, 2, 3, 4, 5, 6}. Also find the inverse element of 4 if it exists. [2019(A)
Solution:
Given set A = { 1, 2, 3, 4, 5, 6} Binary operation ∗ defined on A is X₇.
i.e. a ∗ b = a × b mod 7
= The remainder on dividing a × b by 7
The composition table for this operation is:

∗	1	2	3	4	5	6
1	1	2	3	4	5	6
2	2	4	6	1	3	5
3	3	6	2	5	1	4
4	4	1	5	2	6	3
5	5	3	1	6	4	2
6	6	5	4	3	2	1

As the second row is identical to first row, we have ‘1’ as the identity element.
As 4 ∗ 2 = 2 ∗ 4 = 1 we have 4^-1 = 2

Question 2.
Let R be a relation on the set R of real numbers such that aRb iff a – b is an integer. Test whether R is an equivalence relation. If so, find the equivalence class of 1 and \(\frac{1}{2}\). [2019(A)
Solution:
The relation R on the set of real numbers is defined as
R = { (a, b) : a – b ∈ Z}
Reflexive:
∀ a ∈ R (set of real numbers)
a – a = 0 ∈ Z
⇒ (a, a) ∈ R
⇒ R is reflexive
Symmetric:
Let (a, b) ∈ R
⇒ a – b ∈ Z
⇒ b – a ∈ Z
⇒ (b, a) ∈ R
⇒ R is symmetric.
Transitive:
Let (a, b), (b, c) ∈ R
⇒ a – b and b – c ∈ Z
⇒ a – b + b – c ∈ Z
⇒ a – c ∈ Z
⇒ (a, c) ∈ R
⇒ R is transitive
Thus R is an equivalence relation
[1] = { x ∈ R : x – 1 ∈ Z} = Z
\(\frac{1}{2}\) = { x ∈ R : x – \(\frac{1}{2}\) ∈ Z}
= {x ∈ R : x = \(\frac{2 k+1}{2}\), k ∈ Z}

Question 3.
Two types of food X and Y are mixed to prepare a mixture in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. These vitamins are available in 1 kg of food as per the table given below: [2019(A)

Vitamin
Food	A	B	C
X	1	2	3
Y	2	2	1

1 kg of food X costs ₹16 and 1 kg of food Y costs ₹20. Formulate the LPP so as to determine the least cost of the mixture containing the required amount of vitamins.
Solution:
Let x kg of food X and Y kg of food y are to be mixed to prepare the mixture.
Total cost = 16x + 20y to be minimum.
According to the question
Total vitamin A = x + 2y ≥ 10 units
Total vitamin B = 2x + 2y ≥ 12 units
Total vitamin C = 3x + y ≥ 8 units.
∴ The required LPP is minimize
Z= 16x + 20y
Subject to : x + 2y ≥ 10
x + y ≥ 6
3x + y ≥ 8
x, y ≥ 0

Question 4.
Let ~ be defined by (m, n) ~ (p, q) if mq = np, where m, n, p, q e Z – {0}. Show that it is an equivalence relation. [2018(A)
Solution:
Let A = z – {0}
~ is a relation on A x A defined as (m, n) ~ (p, q) ⇔ mq = np
Reflexive : For all (m, n) ∈ A × A
We have mn = nm
⇒ (m, n) ~ (m, n)
∴ ~ is reflexive.
Symmetric: Let {m, n), (p, q) ∈ A × A and (m, n) ~ (p, q)
⇒ mq = np
⇒ pn = qm
(p, q) ~ (m, n)
∴ ~ is symmetric.
Transitive: Let (m, n), (p, q), (x, y) ∈ A × A
and (m, n) ~ (p, q), (p, q) ~ (x, y)
⇒ mq = np and py = qx
⇒ mqpy = npqx
⇒ my = nx
⇒ (m, n) ~ (x, y)
∴ ~ is transitive.
Thus ~ is an equivalence relation.

Question 5.
Solve the following LPP graphically:
Minimize Z = 4x + 3y
subject to 2x + 5y ≥ 10
x, y ≥ 0. [2018(A)
Solution:
Given LPP is:
Minimize: Z = 4x + 3y
Subject to: 2x + 5y ≥ 10
x, y ≥ 0
Step – 1 Considering the constraints as equations we have 2x + 5y = 10

x	5	0
y	0	2

Let us draw the graph.

Step – 2 As 0(0, 0) does not satisfy 2x + 5y > 0 and x, y > 0 is the first quadrant, we have the shaded region is the feasible region whose vertices are A(5, 0) B(0, 2).
Step – 3 Z (5, 0) = 20
Z (0, 2) = 6 … Minimum
As the feasible region is unbounded. Let us draw the half plane.
4x + 3y < 6

x	0	\(\frac{3}{2}\)
y	2	0

Step – 4 As there is no point common to the feasible region and the half plane 4x + 3y < 6, we have Z is minimum for x = 0, y = 2 and Z(min) = 6

Question 6.
Find the feasible region of the system 2y – x > 0, 6y – 3x < 21, x > 0, y > 0. [2017 (A)
Solution:
Step – 1: Treating the constraints as equations we have
2y – x = 0
6y – 3x = 21
⇒ 2y – x = 0
2y – x = 7
Step – 2: Let us draw the lines.
Table – 1

x	0	2
y	0	1

x	1	37
y	4	5

Step – 3: Clearly A(1, 3) Satisfies both the constraints, x > 0, y > 0 is the first quadrant. Thus the shaded region is the feasible region.

Question 7.
Solve the following LPP graphically:
Maximize: Z = 20x + 30y
Subject to: 3x + 5y ≤ 15
x, y ≥ 0. [2014 (A), 2016 (A), 2017 (A)
Solution:
Given LPP is
Maximize: Z = 20x + 30y
Subject to: 3x + 5y ≤ 15
x, y ≥ 0
Step – 1 Treating the constraints as equations we get 3x + 5y = 15.
Step- 2 Let us draw the graph

x	5	0
y	0	3

Step – 3
As 0(0, 0) satisfies 3x + 5y ≤ 15 the shaded region is the feasible region.
Step – 4
The vertices ofthe feasible region are 0(0, 0), A(5, 0) and B(0, 3).
Z(0) = 0, Z(A) = 100, Z(B) = 90
Z attains maximum at A for x = 5 and y = 0.
The given LPP has a solution, x = 5, y = 0 and Z(max) = 100.

Question 8.
Find the feasible region of the following system:
2x + y ≥ 6, x – y ≤ 3, x ≥ 0, y ≥ 0. [2016 (A)
Solution:
Given system of inequations are
2x + y ≥ 6, x – y ≤ 3, x ≥ 0, y ≥ 0
Step- 1: Consider 2x + y = 6
x – y = 3
Step – 2: Let us draw the graph
Table- 1

x	3	0
y	0	6

Table- 2

x	3	0
y	0	-3

Step – 3: 0(0, 0) satisfies x – y < 3, does not satisfy 2x + y > 6 and x > 0, y > 0 is the first quadrant. Thus the shaded region is the feasible region.

Question 9.
Solve the following LPP graphically:
Minimize: Z = 6x₁ + 7x₂
Subject to: x₁ + 2x₂ ≥ 1
x₁, x₂ ≥ 0. [2015 (A)
Solution:
Given LPP is
Minimize: Z = 6x₁+ 7x₂
Subject to: x₁ + 2x₂ ≥ 2
x₁, x₂ ≥ 0
Let us draw the line x₁ + 2x₂ = 2

x1	0	2
x2	1	0

Clearly (0, 0) does not satisfy x₁ + 2x₂ ≥ 2 and x₁, x₂ ≥ 0 is the first quadrant.
The shaded region is the feasible region.
The coordinates of vertices are A(2, 0) and B(0, 1).

Point	Z = 6x1 + 7x2
A (2, 0)	12
B (0,1)	7 → Minimum

As there is no point common to the half plane 6x₁ + 7x₂ < 7 and the feasible region.
Z is minimum when x₁ = 0, y₁ =1 and the minimum value of z = 7

Question 10.
Find the feasible region of the following system:
2y – x ≥ 0, 6y – 3x ≤ 21, x ≥ 0, y ≥ 0. [2015 (A)
Solution:
Given system is
2y – x ≥ 0
6y – 3x ≤ 21
x, y ≥ 0.
Considering the constraints as equations we have
2y – x = 0
and 6y – 3x = 21

x	0	2
x	0	1

⇒ 3y – x = 7

x	-7	2
x	0	3

Let us draw the lines

Clearly (2, 0) does not satisfy 2y – x ≥ 0 and satisfies 6y – 3x ≤ 21
∴ The shaded region is the feasible region.

Question 11.
Find the maximum value of z = 50x₁ + 60x₂
subject to 2x₁ + 3x₂ ≤ 6
x₁, x₂ ≥ 0. [2013 (A)
Solution:
Let us consider the constraints as equations.
2x₁ + 3x₂ = 6 … (1)
The table of some points on (1) is

x1	0	3
x2	2	0

Let us draw the line 2x₁ + 3x₂ = 6

As (0, 0) satisfies the inequality 2x₁ + 3x₂ ≤ 6 and x₁, x₂ ≥ 0 is the first quadrant, the shaded region is the feasible region with corner points O(0, 0), A(3, 0) and B(0, 2).

Corner point	z = 50x1 + 60x2
O(0, 0)	0
A(3, 0)	150
B(0, 2)	120

Thus Z_(max) = 150 for x₁ = 3, x₂ = 0

Question 12.
Shade the feasible region satisfying the inequations 2x + 3y ≤ 6, x ≥ 0, y ≥ 0 in a rough sketch. [2011(A)
Solution:
Let us consider the line 2x + 3y = 6

x1	0	3
x2	2	0

Let us draw the line on the graph

The feasible region is shaded in the figure.

Question 13.
Show the feasible region for the following constraints in a graph:
2x + y ≤ 4, x ≥ 0, y ≥ 0. [2010(A)
Solution:
Let us draw the graph of 2x + y = 4.

The shaded region shows the feasible region.

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Additional Exercise Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Additional Exercise

(A) Multiple Choice Questions (Mcqs) With Answers

Question 1.
If \(\left|\begin{array}{ccc}
1+x & x & x^2 \\
x & 1+x & x^2 \\
x^2 & x & 1+x
\end{array}\right|\) = a + bx + cx² + dx³ + ex⁴ + fx⁵ then write the value of a.
(a) 0
(b) 2
(c) 1
(d) 3
Answer:
(c) 1

Question 2.
If every element of a third order determinant of value 8 is multiplied by 2, then write the value of the new determinant.
(a) 32
(b) 64
(c) 16
(d) 128
Answer:
(b) 64

Question 3.
If A is a 4 x 5 matrix and B is a matrix such that A^TB and BA^T both are defined, then write the order of B
(a) 4 x 5
(b) 1 x 5
(c) 5 x 4
(d) None of these
Answer:
(a) 4 x 5

Question 4.
If \(\left[\begin{array}{lll}
3 & 5 & 3 \\
2 & 4 & 2 \\
\lambda & 7 & 8
\end{array}\right]\) is a singular matrix, write die value of 1.
(a) λ = 2
(b) λ = 1
(c) λ = 4
(d) λ = 8
Answer:
(d) λ = 8

Question 5.
Determine the maximum value of \(\left|\begin{array}{rl}
\cos x & \sin x \\
-\sin x & \cos x-1
\end{array}\right|\)
(a) 1
(b) 2
(c) 3
(d) 0
Answer:
(b) 2

Question 6.
If \(\left[\begin{array}{cc}
x & y \\
x & \frac{x}{2}+t
\end{array}\right]\) + \(\left[\begin{array}{cc}
y & x+t \\
x+2 & \frac{x}{2}
\end{array}\right]\) = \(\left[\begin{array}{ll}
1 & 4 \\
2 & 3
\end{array}\right]\) then find x.
(a) x = 1
(b) x = 0
(c) x = 2
(d) x = -1
Answer:
(b) x = 0

Question 7.
If \(\left[\begin{array}{cc}
x & y \\
x & \frac{x}{2}+t
\end{array}\right]\) + \(\left[\begin{array}{cc}
y & x+t \\
x+2 & \frac{x}{2}
\end{array}\right]\) = \(\left[\begin{array}{ll}
1 & 4 \\
2 & 3
\end{array}\right]\) then find y.
(a) y = 1
(b) y = 3
(c) y = 2
(d) y = 0
Answer:
(a) y = 1

Question 8.
If \(\left[\begin{array}{cc}
x & y \\
x & \frac{x}{2}+t
\end{array}\right]\) + \(\left[\begin{array}{cc}
y & x+t \\
x+2 & \frac{x}{2}
\end{array}\right]\) = \(\left[\begin{array}{ll}
1 & 4 \\
2 & 3
\end{array}\right]\) then find t.
(a) t = 1
(b) t = 2
(c) t = 3
(d) t = 0
Answer:
(c) t = 3

Question 9.
Which matrix is a unit matrix?
(a) \(\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right)\)
(b) \(\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right)\)
(c) \(\left(\begin{array}{ll}
1 & 1 \\
0 & 1
\end{array}\right)\)
(d) \(\left(\begin{array}{ll}
1 & 1 \\
1 & 1
\end{array}\right)\)
Answer:
(b) \(\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right)\)

Question 10.
If \(\left(\begin{array}{cc}
\mathbf{x}_1 & \mathbf{x}_2 \\
\mathbf{y}_1 & \mathbf{y}_2
\end{array}\right)\) – \(\left(\begin{array}{ll}
2 & 3 \\
0 & 1
\end{array}\right)\) = \(\left(\begin{array}{ll}
3 & 5 \\
1 & 2
\end{array}\right)\) then find x₁, x₂, y₁, y₂.
(a) x₁ = 8, x₂ = 5, y₁ = 3, y₂ = 1
(b) x₁ = 1, x₂ = 8, y₁ = 5, y₂ = 3
(c) x₁ = 5, x₂ = 8, y₁ = 1, y₂ = 3
(d) x₁ = 3, x₂ = 1, y₁ = 8, y₂ = 5
Answer:
(c) x₁ = 5, x₂ = 8, y₁ = 1, y₂ = 3

Question 11.
If \(\left|\begin{array}{ll}
2 & 4 \\
k & 6
\end{array}\right|\) = 0, what is the value of k?
(a) 3
(b) 4
(c) 2
(d) 6
Answer:
(a) 3

Question 12.
If \(\left|\begin{array}{ll}
\mathbf{a}_1 & \mathbf{b}_1 \\
\mathbf{c}_1 & \mathbf{d}_1
\end{array}\right|\) = k \(\left|\begin{array}{ll}
a_1 & c_1 \\
b_1 & d_1
\end{array}\right|\) hen what is the value of k?
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(d) 4

Question 13.
If A = \(\left(\begin{array}{lll}
1 & 0 & 2 \\
5 & 1 & x \\
1 & 1 & 1
\end{array}\right)\) is a singular matrix then what is the value of x?
(a) 6
(b) 7
(c) 8
(d) 9
Answer:
(d) 9

Question 14.
Evaluate \(\left|\begin{array}{ccc}
-6 & 0 & 0 \\
3 & -5 & 7 \\
2 & 8 & 11
\end{array}\right|\)
(a) 66
(b) 666
(c) 6666
(d) 6
Answer:
(b) 666

Question 15.
Evaluate \(\left|\begin{array}{lll}
1 & 1 & b+c \\
1 & b & c+a \\
1 & c & a+b
\end{array}\right|\)
(a) 0
(b) 1
(c) 11
(d) 2
Answer:
(a) 0

Question 16.
Evaluate \(\left|\begin{array}{ccc}
1^2 & 2^2 & 3^2 \\
2^2 & 3^2 & 4^2 \\
3^2 & 4^2 & 5^2
\end{array}\right|\)
(a) 54
(b) 58
(c) -54
(d) 60
Answer:
(c) -54

Question 17.
If A and B are square matrices of order 3, such that |A| = -1, |B| = 3 then |3 AB| = –
(a) 1
(b) 11
(c) 9
(d) 81
Answer:
(d) 81

Question 18.
For what k
x + 2y – 3z = 2
(k + 3)z = 3
(2k + 1)y + z = 2 is inconsistent?
(a) -3
(b) -6
(c) 3
(d) 6
Answer:
(a) -3

Question 19.
The sum of two nonintegral roots of \(\left|\begin{array}{lll}
x & 2 & 5 \\
3 & x & 3 \\
5 & 4 & x
\end{array}\right|\) = 0 is ______.
(a) 5
(b) -5
(c) 3
(d) 15
Answer:
(b) -5

Question 20.
The value of \(\left|\begin{array}{ccc}
1 & 2 & 3 \\
3 & 5 & 2 \\
8 & 14 & 20
\end{array}\right|\) is ______.
(a) 1
(b) 2
(c) 0
(d) 3
Answer:
(c) 0

Question 21.
If [x 1] \(\left[\begin{array}{cc}
1 & 0 \\
-2 & 0
\end{array}\right]\) = 0, then x equals:
(a) 0
(b) -2
(c) -1
(d) 2
Answer:
(d) 2

Question 22.
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:
(a) 27
(b) 18
(c) 81
(d) 512
Answer:
(d) 512

Question 23.
If A = \(\left[\begin{array}{cc}
\cos \alpha & -\sin \alpha \\
\sin \alpha & \cos \alpha
\end{array}\right]\) , and A + A’ = I, then the value of α is
(a) \(\frac{\pi}{6}\)
(b) \(\frac{\pi}{3}\)
(c) π
(d) \(\frac{3 \pi}{2}\)
Answer:
(b) \(\frac{\pi}{3}\)

Question 24.
Matrix A and B will be inverse of each other only if
(a) AB = BA
(b) AB = BA = 0
(c) AB = 0, BA = I
(d) AB = BA = I
Answer:
(d) AB = BA = I

Question 25.
The matrix P = \(\left[\begin{array}{lll}
0 & 0 & 4 \\
0 & 4 & 0 \\
4 & 0 & 0
\end{array}\right]\) is a
(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) None of these
Answer:
(a) square matrix

Question 26.
If A and B are symmetric matrices of same order, then AB – BA is a
(a) Skew-symmetric matrix
(b) Symmetric matrix
(c) Zero matrix
(d) Identity
Answer:
(a) Skew-symmetric matrix

Question 27.
If A is a square matrix of order 3, such that A(adj A) = 10I, then |adj A| is equal to
(a) 1
(b) 10
(c) 100
(d) 1000
Answer:
(c) 100

Question 28.
Let A be a square matrix of order 2 × 2, then |KA| is equal to
(a) K|A|
(b) K²|A|
(c) K³|A|
(d) 2K|A|
Answer:
(b) K²|A|

Question 29.
If A and B are invertible matrices then which of the following is not correct
(a) Adj A = |A|. A^-1
(b) det (A^-1) = (det A)^-1
(c) (AB)^-1 = B^-1A^-1
(d) (A + B)^-1 = A^-1 + B^-1
Answer:
(d) (A + B)^-1 = A^-1 + B^-1

Question 30.
If A is a skew-symmetric matrix of order 3, then the value of |A| is
(a) 3
(b) 0
(c) 9
(d) 27
Answer:
(b) 0

Question 31.
If A is a square matrix of order 3, such that A(adjA) = 10I, then ladj Al is equal to
(a) 1
(b) 10
(c) 100
(d) 1000
Answer:
(c) 100

Question 32.
Let A be a non-angular square matrix of order 3 x 3, then |A. adj Al is equal to
(a) |A|³
(b) |A|²
(c) |A|
(d) 3|A|
Answer:
(a) |A|³

Question 33.
Let A be a square matrix of order 3 × 3 and k a scalar, then |kA| is equal to
(a) k|A|
(b) |k||A|
(c) k³|A|
(d) none of these
Answer:
(c) k³|A|

Question 34.
If a, b, c are all distinct, and \(\left|\begin{array}{lll}
a & a^2 & 1+a^3 \\
b & b^2 & 1+b^3 \\
c & c^2 & 1+c^3
\end{array}\right|\) = 0 then the value of abc is
(a) 0
(b) -1
(c) 3
(d) -3
Answer:
(b) -1

Question 35.
If a, b, c are in AP, then the value of \(\left|\begin{array}{lll}
x+1 & x+2 & x+a \\
x+2 & x+3 & x+b \\
x+3 & x+4 & x+c
\end{array}\right|\) is:
(a) 4
(b) -3
(c) 0
(d) abc
Answer:
(c) 0

Question 36.
If A is a skew-symmetric matrix of order 3, then the value of |A| is
(a) 3
(b) 0
(c) 9
(d) 27
Answer:
(b) 0

Question 37.
A bag contains 3 white, 4 black and 2 red balls. If 2 balls are choosen at random (without replacement), then the probability that both the balls are white is:
(a) \(\frac{1}{18}\)
(b) \(\frac{2}{9}\)
(c) \(\frac{1}{12}\)
(d) \(\frac{1}{24}\)
Answer:
(c) \(\frac{1}{12}\)

Question 38.
Three diece are thrown simultaneously. The probability of obtaining a total score of 5 is:
(a) \(\frac{5}{216}\)
(b) \(\frac{1}{6}\)
(c) \(\frac{1}{36}\)
(d) \(\frac{1}{49}\)
Answer:
(c) \(\frac{1}{36}\)

Question 39.
An urn contains 6 balls of which two are red and four are black. Two balls are drawn at random. Probability that they are of the different colour is:
(a) \(\frac{2}{5}\)
(b) \(\frac{1}{15}\)
(c) \(\frac{8}{15}\)
(d) \(\frac{4}{15}\)
Answer:
(d) \(\frac{4}{15}\)

Question 40.
The probability of obtaining an even prime number on each die when a pair of dice is rolled is:
(a) 0
(b) \(\frac{1}{3}\)
(c) \(\frac{1}{12}\)
(d) \(\frac{1}{36}\)
Answer:
(d) \(\frac{1}{36}\)

Question 41.
Two events A and B are said to be independent if:
(a) A and B are mutually exclusive
(b) P (A’B’) = [1 – P(A)][1 – P(B)]
(c) P(A) = P(B)
(d) P(A) + P(B) = 1
Answer:
(b) P (A’B’) = [1 – P(A)][1 – P(B)]

Question 42.
A die is. thrown once, then the probability of getting number greater than 3 is:
(a) \(\frac{1}{2}\)
(b) \(\frac{2}{3}\)
(c) 6
(d) 0
Answer:
(a) \(\frac{1}{2}\)

Question 43.
If P(A) = \(\frac{6}{11}\), P(B) = \(\frac{5}{11}\) and P(A ∪ B) = \(\frac{7}{11}\), then P(A/B) is:
(a) \(\frac{2}{5}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{4}{5}\)
(d) 1
Answer:
(c) \(\frac{4}{5}\)

Question 44.
Let the target be hit A and B: the target be hit by B and C: the target be hit by A and C. Then the probability that A, B and C all will hit, is:
(a) \(\frac{4}{5}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{2}{5}\)
(d) \(\frac{1}{5}\)
Answer:
(c) \(\frac{2}{5}\)

Question 45.
What is the probability that ‘none of them will hit the target’?
(a) \(\frac{1}{30}\)
(b) \(\frac{1}{60}\)
(c) \(\frac{1}{15}\)
(d) \(\frac{2}{15}\)
Answer:
(b) \(\frac{1}{60}\)

(B) Very Short Type Questions With Answers

Question 1.
If \(\left|\begin{array}{ccc}
1+\mathbf{x} & \mathbf{x} & \mathbf{x}^2 \\
\mathbf{x} & 1+\mathbf{x} & \mathbf{x}^2 \\
\mathbf{x}^2 & \mathbf{x} & 1+\mathbf{x}
\end{array}\right|\) = a + bx + cx² + dx³ + ex⁴ + fx⁵ then write the value of a.
Solution:
\(\left|\begin{array}{ccc}
1+\mathbf{x} & \mathbf{x} & \mathbf{x}^2 \\
\mathbf{x} & 1+\mathbf{x} & \mathbf{x}^2 \\
\mathbf{x}^2 & \mathbf{x} & 1+\mathbf{x}
\end{array}\right|\)
= a + bx + cx² + dx³ + ex⁴ + fx⁵
which is an identity
Putting x = 0 we get
a = \(\left|\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right|\) = 1

Question 2.
If every element of a third order determinant of value 8 is multiplied by 2, then write the value of the new determinant.
Solution:
According to the question
|A| = 8
Now |KA| = Kⁿ|A|
⇒ |2A| = 2³|A| = 8 × 8 = 64
Value of the new determinant is 64.

Question 3.
If I is an identity matrix of order n, then k being a natural number, write the matrix I^k_n.
Solution:
If I is an identity matrix of order n, then I^k_n = I_n

Question 4.
If A is a 4 × 5 matrix and B is a matrix such that A^TB and BA^T both are defined, then write the order of B.
Solution:
Order of A = 4 × 5
Order of A^T = 5 × 4
Let order of B = m × n
A^TB is well defined ⇒ m = 4
BA^T is well defined ⇒ n = 5
Order of B = 4 × 5

Question 5.
Write the matrix which when added to the matrix \(\left[\begin{array}{cc}
2 & -3 \\
-4 & 7
\end{array}\right]\) gives the matrix \(\left[\begin{array}{ll}
4 & 1 \\
3 & 2
\end{array}\right]\)
Solution:
Let the required matrix is A.
\(\left(\begin{array}{cc}
2 & -3 \\
-4 & 7
\end{array}\right)\) + A = \(\left(\begin{array}{ll}
4 & 1 \\
3 & 2
\end{array}\right)\)
A = \(\left(\begin{array}{ll}
4 & 1 \\
3 & 2
\end{array}\right)\) – \(\left(\begin{array}{cc}
2 & -3 \\
-4 & 7
\end{array}\right)\) = \(\left(\begin{array}{cc}
2 & 4 \\
7 & -5
\end{array}\right)\)

Question 6.
Determine the maximum value of \(\left|\begin{array}{rl}
\cos x & \sin x \\
-\sin x & \cos x-1
\end{array}\right|\)
Solution:
Let f(x) = \(\left|\begin{array}{rl}
\cos x & \sin x \\
-\sin x & \cos x-1
\end{array}\right|\)
= cos²x – cos x + sin²x = 1 – cos x
As – 1 < cos x ≤ 1
⇒ 1 >- cos x ≥ – 1
⇒ 2 > 1 – cos x ≥ 0
The maximum value of f(x) = 2.

Question 7.
Write the value of k if:
\(\left|\begin{array}{lll}
\mathbf{a a _ { 1 }} & \mathbf{a a}_2 & \mathbf{a} \mathbf{a}_3 \\
\mathbf{a b _ { 1 }} & \mathbf{a b}_2 & \mathbf{a b} \\
\mathbf{a c _ { 2 }} & \mathbf{a c}_2 & \mathbf{a c _ { 3 }}
\end{array}\right|\) = k\(\left|\begin{array}{lll}
\mathbf{a}_1 & \mathbf{b}_1 & \mathbf{c}_1 \\
\mathbf{a}_2 & \mathbf{b}_2 & \mathbf{c}_2 \\
\mathbf{a}_3 & \mathbf{b}_3 & \mathbf{c}_3
\end{array}\right|\)
Solution:
\(\left|\begin{array}{lll}
\mathbf{a a _ { 1 }} & \mathbf{a a}_2 & \mathbf{a} \mathbf{a}_3 \\
\mathbf{a b _ { 1 }} & \mathbf{a b}_2 & \mathbf{a b} \\
\mathbf{a c _ { 2 }} & \mathbf{a c}_2 & \mathbf{a c _ { 3 }}
\end{array}\right|\) = k\(\left|\begin{array}{lll}
\mathbf{a}_1 & \mathbf{b}_1 & \mathbf{c}_1 \\
\mathbf{a}_2 & \mathbf{b}_2 & \mathbf{c}_2 \\
\mathbf{a}_3 & \mathbf{b}_3 & \mathbf{c}_3
\end{array}\right|\)
k = a³.

Question 8.
If A is a 3 × 3 matrix and |A| = 3, then write the matrix represented by A × adj A.
Solution:
|A| = 3 ⇒ A × Adj A = \(\left(\begin{array}{lll}
3 & 0 & 0 \\
0 & 3 & 0 \\
0 & 0 & 3
\end{array}\right)\)

Question 9.
If ω is a complex cube root of 1, then for what value of λ the determinant
\(\left|\begin{array}{ccc}
1 & \omega & \omega^2 \\
\omega & \lambda & 1 \\
\omega^2 & 1 & \omega
\end{array}\right|\) = 0?
Solution:

⇒ for any value of ‘A,’ the given determinant is ‘0’

Question 10.
If [1 2 3] A = [0], then what is the der of the matrix A?
Solution:
If [1 2 3] A = [0]
A is a 3 × 1 matrix

Question 11.
What is A + B if A = \(\left(\begin{array}{cc}
1 & 2 \\
3 & -1
\end{array}\right)\), B = \(\left(\begin{array}{cc}
0 & -1 \\
-2 & 1
\end{array}\right)\)?
Solution:
For A = \(\left(\begin{array}{cc}
1 & 2 \\
3 & -1
\end{array}\right)\), B = \(\left(\begin{array}{cc}
0 & -1 \\
-2 & 1
\end{array}\right)\)
A + B = \(\left(\begin{array}{ll}
1 & 1 \\
1 & 0
\end{array}\right)\)

Question 12.
Give an example of a unit matrix.
Solution:
\(\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right)\) is a unit matrix of 2nd order.

Question 13.
Construct a 2 × 3 matrix having elements defined by a_ij = i – j.
Solution:
a_ij = i – j
a₁₁ =0, a₁₂ = 1 – 2 = – 1, a₁₃ = 1 – 3 =- 2
a₂₁ = 2 – 1 = 1, a₂₂ = 2 – 2 = 0, a₂₃ = 2 – 3 = -1
∴ The required matrix is \(\left(\begin{array}{ccc}
0 & -1 & -2 \\
0 & 0 & -1
\end{array}\right)\).

Question 14.
Find x, y if A = A’ where A = \(\left(\begin{array}{ll}
5 & \mathbf{x} \\
\mathbf{y} & 0
\end{array}\right)\)
Solution:
A = A’
⇒ \(\left(\begin{array}{ll}
5 & \mathbf{x} \\
\mathbf{y} & 0
\end{array}\right)\) = \(\left(\begin{array}{ll}
5 & \mathbf{y} \\
\mathbf{x} & 0
\end{array}\right)\) ⇒ x = y
∴ x and y are any real number where x = y

Question 15.
Cana matrix be constructed by taking 29 elements?
Solution:
Only two matrices can be formed by taking 29 elements. They are of order 1 × 29 and 29 × 1.

Question 16.
If \(\left|\begin{array}{ll}
2 & 4 \\
k & 6
\end{array}\right|\) = 0 , what is the value of k?
Solution:
\(\left|\begin{array}{ll}
2 & 4 \\
k & 6
\end{array}\right|\) = 0 ⇒ 12 – 4k = 0 ⇒ k = 3

Question 17.
If \(\left|\begin{array}{ll}
\mathbf{a}_1 & \mathbf{b}_1 \\
\mathbf{c}_{\mathbf{1}} & \mathbf{d}_1
\end{array}\right|\) = k = \(\left|\begin{array}{ll}
\mathbf{a}_1 & \mathbf{c}_1 \\
\mathbf{b}_1 & \mathbf{d}_1
\end{array}\right|\) then what is the value of k?
Solution:
k = 1

Question 18.
If A and B are square matrices of order 3, such that |A| = -1, |B| = 3 then |3 AB| = ______.
Solution:
|3 AB| = 27 |A| |B| = 81

Question 19.
Solve: \(\left|\begin{array}{ccc}
2 & 2 & x \\
-1 & x & 4 \\
1 & 1 & 1
\end{array}\right|\) = 0
Solution:
\(\left|\begin{array}{ccc}
2 & 2 & x \\
-1 & x & 4 \\
1 & 1 & 1
\end{array}\right|\) = 0 => \(\left|\begin{array}{ccc}
0 & 2 & x \\
-1-x & x & 4 \\
0 & 1 & 1
\end{array}\right|\) = 0
⇒ – (- 1 – x) (2 – x) = 0 ⇒ x = -1, x = 2.

(C) Short Type Questions With Answers

Question 1.
If A = \(\left[\begin{array}{ccc}
1 & 2 & 3 \\
3 & -2 & 1 \\
4 & 2 & 1
\end{array}\right]\) then show that A³ – 23A – 40I = 0
Solution:

Question 2.
Solve: \(\left|\begin{array}{ccc}
\mathbf{x + 1} & \omega & \omega \\
\omega & x+\omega^2 & 1 \\
\omega^2 & 1 & x+\omega
\end{array}\right|\) = 0
Solution:

Question 3.
If A = \(\left[\begin{array}{ccc}
1 & 2 & 0 \\
0 & 1 & 3 \\
-2 & 5 & 3
\end{array}\right]\), then verify that A + A’ is symmetric and A – A’ is skew symmetric.
Solution:

Question 4.
If A, B, C are matrices of order 2 × 2 each and 2A + B + C = \(\left[\begin{array}{ll}
1 & 2 \\
3 & 0
\end{array}\right]\), A + B + C = \(\left[\begin{array}{ll}
0 & 1 \\
2 & 1
\end{array}\right]\) and A + B – C = \(\left[\begin{array}{ll}
1 & 2 \\
1 & 0
\end{array}\right]\), then find A, B and C.
Solution:

Question 5.
Find the inverse of the following matrix: \(\left[\begin{array}{lll}
1 & 1 & 2 \\
0 & 1 & 2 \\
1 & 2 & 1
\end{array}\right]\)
Solution:
Let A = \(\left[\begin{array}{lll}
1 & 1 & 2 \\
0 & 1 & 2 \\
1 & 2 & 1
\end{array}\right]\)
Method – I
Let us find A^-1 by using elementary row transformation.
Let A = IA

Method – II
|A| = 1(1 – 4) – 1(0- 2) + 2(0- 1)
= 1(-3) – 1(-2) + 2(-1)
= -3 ≠ 0
∴ A^-1 exists.
A₁₁ = -3, A₁₂ = 2, A₁₃ = -1

Question 6.
Show that \(\left|\begin{array}{ccc}
a-b-c & 2 a & 2 a \\
2 b & b-c-a & 2 b \\
2 c & 2 c & c-a-b
\end{array}\right|\) = (a+b +c)³
Solution:

= (a + b + c)³ (1 – 0) = (a + b + c)³

Question 7.
Find the inverse of the following matrix: \(\left[\begin{array}{lll}
0 & 0 & 2 \\
0 & 2 & 0 \\
2 & 0 & 0
\end{array}\right]\)
Solution:
A = \(\left[\begin{array}{lll}
0 & 0 & 2 \\
0 & 2 & 0 \\
2 & 0 & 0
\end{array}\right]\)
|A| = 2(- 4) = – 8 ≠ 0
∴ A^-1 exists.
A₁₁ = 0, A₁₂ = 0, A₁₃ = – 4
A₂₁ = 0, A₂₂ = – 4, A₂₃ = 0
A₃₁ = 0,A₃₂ = 0, A₃₃ = – 4
∴ The matrix of cofactors

Question 8.
If the matrix A is such that \(\left[\begin{array}{cc}
1 & -1 \\
2 & 3
\end{array}\right]\)A = \(\left[\begin{array}{cc}
-4 & 1 \\
7 & 7
\end{array}\right]\), find A.
Solution:

Question 9.
Show that (a + 1) is a factor of \(\left|\begin{array}{ccc}
a+1 & 2 & 3 \\
1 & a+1 & 3 \\
3 & -6 & a+1
\end{array}\right|\).
Solution:

= (a + 1) (a² + 2a + 1 + 18) – 2(a + 1 – 9) + 3(-6 – 3a – 3)
= (a + 1)(a² + 2a + 19) – 2a + 16 – 27 – 9a
= (a + 1) (a² + 2a + 19) – 11a – 11
= (a + 1) (a² + 2a + 19) – 11(a + 1)
= (a + 1) (a² + 2a + 8)
⇒ (a + 1) is a factor of the given determinant.

Question 11.
If A = \(\left[\begin{array}{ll}
\alpha & 0 \\
1 & 1
\end{array}\right]\) and B = \(\left[\begin{array}{ll}
1 & 0 \\
5 & 1
\end{array}\right]\) show that for no values of α, A² = B.
Solution:

⇒ α2 = 1 and α + 1 = 5
⇒ α = ± 1 and α = 4
Which is not possible.
There is no α for which A² = B

Question 12.
If A = \(\left[\begin{array}{ll}
3 & -4 \\
1 & -1
\end{array}\right]\), then show that A^k = \(\left[\begin{array}{cc}
1+2 \mathrm{k} & -4 \mathrm{k} \\
\mathrm{k} & 1-2 \mathrm{k}
\end{array}\right]\), k ∈ N.
Solution:

Question 13.
If A = \(\left[\begin{array}{ccc}
1 & -2 & 2 \\
3 & 1 & -1
\end{array}\right]\), B = \(\left[\begin{array}{cc}
2 & 4 \\
1 & 2 \\
3 & -1
\end{array}\right]\), verify that (AB)^T = B^TA^T.

Question 14.
Show that for each real value of λ the system of equations
(λ + 3) + λy = 0
x + (2λ + 5)y = 0 has a unique solution.
Solution:
Given system of equations is a
homogeneous system of linear
equations.
Now
Δ = \(\left|\begin{array}{cc}
\lambda+3 & \lambda \\
1 & 2 \lambda+5
\end{array}\right|\)
= (λ + 3)(2λ + 5) – λ
= 2λ² + 11λ + 15 – λ
= 2λ² + 10λ + 15
As for 2λ² + 10A + 15, D = 100 – 120 < 0
the polynomial 2λ² + 10λ + 15 has no roots i.e. Δ ≠ 0.
Thus the system has a unique trivial solution for every real value of λ.

Question 15.
If A and B are square matrices of same order then show by means of an example that AB ≠ BA in general.
Solution:

∴ AB ≠ BA we have AB ≠ BA in general.

Question 16.
If A = \(\left|\begin{array}{cc}
0 & -\tan \frac{\theta}{2} \\
\tan \frac{\theta}{2} & 0
\end{array}\right|\), then prove that det{(I + A)(I – A)-1} = 1
Solution:

Question 17.
Solve for x: \(\left|\begin{array}{ccc}
15-2 x & 11 & 10 \\
11-3 x & 17 & 16 \\
7-x & 14 & 13
\end{array}\right|\) = 0
Solution:

Question 18.
If A = \(\left[\begin{array}{ccc}
-1 & 3 & 5 \\
1 & -3 & -5 \\
-1 & 3 & 5
\end{array}\right]\) find A³ – A².
Solution:

A² = A ⇒ A²A = A²
⇒ A³ – A² = 0

Question 19.
Prove that: A = \(\left|\begin{array}{ccc}
2 & 3 & 4 \\
1 & -2 & -3 \\
3 & 1 & -8
\end{array}\right|\) ⇒ A² – 5A + 71 = 0.
Solution:

Question 20.
Test whether the following system of equations have non-zero solution.
Write the solution set:
2x + 3y + 4z = 0,
x – 2y – 3z = 0,
3x + y – 8z = 0.
Solution:
Given equations are
2x + 3y + 4z = 0
x – 2y – 3z = 0
3x + y – 8z = 0
Now \(\left|\begin{array}{ccc}
2 & 3 & 4 \\
1 & -2 & -3 \\
3 & 1 & -8
\end{array}\right|\)
= 2(19) – 3(1) + 4(7) 0
∴ The system has no non-zero solution.
The solution set is x = 0; y = 0, z = 0.

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Exercise 6(a)

Question 1.
Two balls are drawn from a bag containing 5 white and 7 black balls. Find the probability of selecting 2 white balls if
Solution:
Two balls are drawn from a bag containing 5 white and 7 black balls.
∴ |S| = 12.

(i) the first ball is replaced before drawing the second.
Solution:
The 1st ball is replaced before the 2nd ball is drawn. We are to select 2 white balls. So in both the draws we will get white balls. Drawing a white ball in 1st draw and in 2nd draw are independent events.
Probability of getting 2 white balls = \(\frac{5}{12}\) × \(\frac{5}{12}\) = \(\frac{25}{144}\)

(ii) the first ball is not replaced before drawing the second.
Solution:
Here the 1st ball is not replaced before the 2nd ball is drawn. Since we are to get 2 white balls in each draw, we must get a white ball.
Now probability of getting a white ball in 1st draw = \(\frac{5}{12}\).
Probability of getting a white ball in 2nd = \(\frac{4}{11}\).
Since the two draws are independent, we have the probability of getting 2 white balls
= \(\frac{5}{12}\) × \(\frac{4}{11}\) = \(\frac{20}{132}\).

Question 2.
Two cards are drawn from a pack of 52 cards; find the probability that
(i) they are of different suits.
(ii) they are of different denominations.
Solution:
Two cards are drawn from a pack of 52 cards. The cards are drawn one after another. Each suit has 13 cards.
|S| = ⁵²C₂
(i) As the two cards are of different suits, their probability
= \(\frac{52}{52}\) × \(\frac{39}{51}\)
(ii) Each denomination contains 4 cards. As the two cards drawn are of different denominations, their probability
= \(\frac{52}{52}\) × \(\frac{48}{51}\)

Question 3.
Do both parts of problem 2 if 3 cards drawn at random.
Solution:
(i) 3 cards are drawn one after another. As they are of different suits, we have their probability
= \(\frac{52}{52}\) × \(\frac{39}{51}\) × \(\frac{26}{50}\).
(ii) As the 3 cards are of different denominations, we have their probability
= \(\frac{52}{52}\) × \(\frac{48}{51}\) × \(\frac{44}{50}\).

Question 4.
Do both parts of problem 2 if 4 cards are drawn at random.
Solution:
(i) 4 cards are drawn one after another. As they are of different suits, we have their probability
= \(\frac{52}{52}\) × \(\frac{39}{51}\) × \(\frac{26}{50}\) × \(\frac{13}{49}\).
(ii) As the cards are of different denominations, we have their probability
= \(\frac{52}{52}\) × \(\frac{48}{51}\) × \(\frac{44}{50}\) × \(\frac{40}{49}\).

Question 5.
A lot contains 15 items of which 5 are defective. If three items are drawn at random, find the probability that
(i) all three are defective
(ii) none of the three is defective.
Do this problem directly.
Solution:
(i) A lot contains 15 items of which 5 are defective. Three items are drawn at random. As the items are drawn one after another.
Their probability = \(\frac{5}{15}\) × \(\frac{4}{14}\) × \(\frac{3}{13}\)
(ii) As none of the 3 items are defective, we have to draw 3 non-defective items one after another.
Their probability = \(\frac{10}{15}\) × \(\frac{9}{14}\) × \(\frac{8}{13}\)

Question 6.
A pair of dice is thrown. Find the probability of getting a sum of at least 9 if 5 appears on at least one of the dice.
Solution:
A pair of dice is thrown. Let A be the event of getting at least 9 points and B, the event that 5 appears on at least one of the dice.
∴ B = {(1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6)}
A = {(3, 6), (4, 5), (5, 4), (6, 3), (4, 6), (5, 5), (6, 4), (5, 6), (6, 5), (6, 6)}
∴ A ∩ B = {(4, 5), (5, 4), (5, 5), (5, 6), (6, 5)}
∴ P (A | B) = \(\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}\) = \(\frac{\frac{5}{36}}{\frac{31}{36}}\) = \(\frac{5}{11}\)

Question 7.
A pair of dice is thrown. If the two numbers appearing are different, find the probability that
(i) the sum of points is 8.
(ii) the sum of points exceeds 8.
(iii) 6 appears on one die.
Solution:
A pair of dice is thrown as two numbers are different
We have |S| = 30
(i) Let A be the. event that the sum of points on the dice is 8, where the numbers on the dice are different.
A = {(2, 6), (3, 5), (5, 3), (6, 2)}
P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}\) = \(\frac{4}{30}\)
(ii) Let B be the event that sum of the points exceeds 8.
B = {(3, 6), (4, 5), (5, 4), (6, 3), (5, 6), (6, 5), (4, 6), (6, 4)}
P(B) = \(\frac{|\mathrm{B}|}{|\mathrm{S}|}\) = \(\frac{8}{30}\)
(iii) Let C be the event that 6 appears on one die.
C = {(1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)}
P(C) = \(\frac{|\mathrm{C}|}{|\mathrm{S}|}\) = \(\frac{10}{30}\) = \(\frac{1}{3}\)

Question 8.
In a class 30% of the students fail in Mathematics, 20% of the students fail in English and 10% fail in both. A student is selected at random.
Solution:
In a class 30% of the students fail in Mathematics, 20% of the students fail in English and 10% fail in both. Let A be the event that a student fails in Mathematics and B be the events that he fails in English.
P(A) = \(\frac{30}{100}\), P(B) = \(\frac{20}{100}\)
Where |S| = 100, P (A ∩ B) = \(\frac{10}{100}\)

(i) If he has failed in English, what is the probability that he has failed in Mathematics?
Solution:
If he has failed in English, then the probability that he has failed in Mathematics.
i.e., P\(\left(\frac{A}{B}\right)\) = \(\frac{P(A \cap B)}{P(B)}\) = \(\frac{\frac{10}{100}}{\frac{20}{100}}\) = \(\frac{1}{2}\)

(ii) If he has failed in Mathematics, what is the probability that he has failed in English?
Solution:
If he has failed in Mathematics, then the probability that he has failed in English
i.e., P\(\left(\frac{B}{A}\right)\) = \(\frac{P(A \cap B)}{P(A)}\) = \(\frac{\frac{10}{100}}{\frac{30}{100}}\) = \(\frac{1}{3}\)

(iii) What is the probability that he has failed in both?
Solution:
Probability that he has failed in both
i.e., P (A ∩ B) = \(\frac{10}{100}\) = \(\frac{1}{10}\)

Question 9.
IfA, B are two events such that
P(A) = 0.3, P(B) = 0.4, P (A ∪ B) = 0.6
Find
(i) P (A | B)
(ii) P (B | A)
(iii) P (A | B^c)
(iv) P (B | A^c)
Solution:
A and B are two set events such that
P(A) = 0.3, P(B) = 0.4, P (A ∪ B) = 0.6
We have
P (A ∪ B) = P(A) + P(B) – P (A ∩ B)
or, 0.6 = 0.3 + 0.4 – P (A ∩ B)
or, P (A ∩ B) = 0.7 – 0.6 = 0.1

Question 10.
If A, B are events such that P(A) = 0.6, P(B) = 0.4 and P (A ∩ B) = 0.2, then find
(i) P (A | B)
(ii) P (B | A)
(iii) P (A | B^c)
(iv) P (B | A^c)
Solution:
A and B are events such that
P(A) = 0.6, P(B) = 0.4, P (A ∩ B) = 0.2

Question 11.
If A and B are independent events, show that
(i) A^c and B^c are independent,
(ii) A and B^c are independent,
(iii) A^c and B are independent.
Solution:
A and B are independent events.
(i) We have P (A ∩ B) = P(A). P(B)
P (A’ ∩ B’) = P (A ∪ B)’ = 1 – P (A ∪ B)
= 1 – [P(A) + P(B) – P (A ∩ B)]
= 1 – P(A) – P(B) + P(A) P(B)
= 1 [1 – P(A)] – P(B) [1 – P(A)]
= [1 – P(A)] [1 – P(B)] = P(A’) P(B’)
∴ A’ and B’ are independent events.

(ii) P (A ∩ B^c) = P (A – B)
= P(A) – P (A ∩ B)
= P(A) – P(A) P(B)
= P(A) [1 – P(B)]
= P(A). P(B^c).
∴ A and B^c are independent events.

(iii) P (A^c ∪ B) = P (B – A)
= P(B) – P (A ∩ B)
= P(B) – P(A) P(B)
= P(B) [1 – P(A)] = P(B) P(A^c)
∴ A^c and B are independent events.

Question 12.
Two different digits are selected at random from the digits 1 through 9.
(i) If the sum is even, what is the probability that 3 is one of the digits selected?
(ii) If the sum is odd, what is the probability that 3 is one of the digits selected?
(iii) If 3 is one of the digits selected, what is the probability that the sum is odd?
(iv) If 3 is one of the digits selected, what is the probability that the sum is even?
Solution:
Two different digits are selected at random from the digits 1 through 9.
(i) Let A be the event that the sum is even and B be the event that 3 is one of the number selected.
We have to find P (B | A).
There are 4 even digits and 5 odd digits.
∴ The sum is even if both the numbers are odd or both are even.
∴ |A| = ⁴C₂ + ⁵C₂ = 6 + 10 = 16
∴ P(A) = \(\frac{16}{{ }^9 \mathrm{C}_2}\) = \(\frac{16}{36}\)
Also B = {(1, 3), (5, 3), (7, 3), (9, 3), (3, 2), (3, 4), (3, 8), (3, 6)}
∴ A ∩ B = {(1, 3), (5, 3), (7, 3), (9, 3)}
P(B) = \(\frac{8}{36}\) P (A ∩ B) = \(\frac{4}{36}\)
P(\(\frac{B}{A}\)) = \(\frac{P(A \cap B)}{P(A)}\) = \(\frac{\frac{4}{36}}{\frac{16}{36}}\) = \(\frac{1}{4}\)

(ii) Let A be the event that the sum is odd. The sum is odd if one of the numbers selected is odd and other is even.
∴ P(A) = \(\frac{5}{9}\) × \(\frac{4}{8}\) + \(\frac{4}{9}\) × \(\frac{5}{8}\) = \(\frac{20}{36}\)
Let B be the event that one of the numbers selected is 3.
∴ B = {(1, 3), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 3), (9, 3)}
∴ A ∩ B = {(2, 3), (4, 3), (6, 3), (8, 3)}

Question 13.
If P(A) = 0.4, P (B | A) = 0.3 and P (B^c | A^c) = 0.2. find
(i) P (A | B)
(ii) P (B | A^c)
(iii) P(B)
(iv) P(A^c)
(v) P (A ∪ B)
Solution:
P(A) = 0.4, P (B | A) = 0.3 and P (B^c | A^c) = 0.2.


(iii) P(B) = 0.6
= \( \frac{6}{10} \)
= \( \frac{3}{5} \)

(iv) P(A^c) = 1 – P(A)
= 1 – 0.4 = 0.6
= \( \frac{6}{10} \) = \( \frac{3}{5} \)

(v) P (A ∪ B) = P(A) + P(B) – P (A ∩ B)
= 0.4 + 0.6 – 0.12
= 1.0 – 0.12 = 0.88

Question 14.
If P(A) = 0.6, P (B | A) = 0.5, find P (A ∪ B) if A, B are independent.
Solution:
P(A) = 0.6, P (B | A) = 0.5
We have P (B | A) = \(\frac{\mathrm{P}(\mathrm{B} \cap \mathrm{A})}{\mathrm{P}(\mathrm{A})}\) = 0.5
or, P (B ∩ A) = 0.5 × P(A)
= 0.5 × 0.6 = 0.3
As A and B are independent events, we have
P (B ∩ A) = P(B) P(A) = 0.3
or, P(B) = \(\frac{0.3}{\mathrm{P}(\mathrm{A})}\)
= \(\frac{0.3}{0.6}\)
= \(\frac{1}{2}\) = 0.5
P (A ∪ B) = P(A) + P(B) – P(A ∩ B)
= 0.6 + 0.5 – 0.3 = 0.8

Question 15.
Two cards are drawn in succession from a deck of 52 cards. What is the probability that both cards are of denomination greater than 2 and less than 9?
Solution:
Two cards are drawn in succession from a deck of 52 cards.
There are 6 denominations which are greater than 2 and less than 9. So there are 24 cards whose denominations are greater than 2 and less than 9.
∴ Their probability = \(\frac{24}{52}\) × \(\frac{23}{51}\).

Question 16.
From a bag containing 5 black and 7 white balls, 3 balls are drawn in succession. Find the probability that
(i) all three are of the same colour.
(ii) each colour is represented.
Solution:
From a bag containing 5 black and 7 white balls, 3 balls are drawn in succession.
(i) The 3 balls drawn are of same colour.
∴ Probability of drawing 3 balls of black colour
= \(\frac{5}{12}\) × \(\frac{4}{11}\) × \(\frac{3}{10}\) = \(\frac{1}{22}\)
Probability of drawing 3 white balls
= \(\frac{7}{12}\) × \(\frac{6}{11}\) × \(\frac{5}{10}\) = \(\frac{7}{44}\)
∴ Probability of drawing 3 balls of same colour
= \(\frac{5}{12}\) × \(\frac{4}{11}\) × \(\frac{3}{10}\) + \(\frac{7}{12}\) × \(\frac{6}{11}\) × \(\frac{5}{10}\) = \(\frac{9}{44}\)

(ii) Balls of both colour will be drawn. If B represents black ball and W represents the white ball.
∴ The possible draws are WWB, WBW, BWW.

Question 17.
A die is rolled until a 6 is obtained. What is the probability that
(i) you end up in the second roll
(ii) you end up in the third roll.
Solution:
A die is rolled until a 6 is obtained
(i) We are to end up in the 2nd roll i.e., we get 6 in the 2nd roll. Let A be the event of getting a 6 in one roll of a die.
∴ P(A) = \(\frac{1}{6}\) ⇒ P(A’) = 1 – \(\frac{1}{6}\) = \(\frac{5}{6}\)
∴ Probability of getting a 6 in the 2nd roll
= \(\frac{5}{6}\) × \(\frac{1}{6}\) = \(\frac{5}{36}\)
(ii) Probability of getting a 6 in the 3rd roll
= \(\frac{5}{6}\) × \(\frac{5}{6}\) × \(\frac{1}{6}\) = \(\frac{25}{216}\)

Question 18.
A person takes 3 tests in succession. The probability of his (her) passing the first test is 0.8. The probability of passing each successive test is 0.8 or 0.5 according as he passes or fails the preceding test. Find the probability of his (her) passing at least 2 tests.
Solution:
A person takes 3 tests in succession. The probability of his passing the 1st test is 0.8. The probability of passing each successive test is 0.8 or 0.5 according as he passes or fails the preceding test.
Let S denotes the success (passing) in a test and F denotes the failure in a test.
∴ P(S) = 0.8
∴ P(F) = 1 – P(S) = 1 – 0.8 = 0.2
We have the following mutually exclusive cases:

Event			Probability
S	S	S	0.8 × 0.8 × 0.8 = 0.512
S	S	F	0.8 × 0.8 × 0.2 = 0.128
S	F	S	0.8 × 0.2 × 0.5 = 0.080
F	S	S	0.2 × 0.5 x 0.8 = 0.080

∴ Probability of atleast 2 successes
= 0.512 + 0.128 + 0.080 + 0.080
= 0.8 = \(\frac{4}{5}\)

Question 19.
A person takes 4 tests in succession. The probability of his passing the first test is p, that of his passing each succeeding test is p or y depending on his passing or failing the preceding test. Find the probability of his passing
(i) at least three test
(ii) just three tests.
Solution:
A person takes 4 tests in succession. The probability of his passing the 1st test is P, that of his passing each succeeding test is P or P/2 depending bn his passing or failing the preceding test. Let S and F denotes the success and failure in the test.
∴ P(S) = P, P(F) = 1 – P
We have the following mutually exclusive tests:

Question 20.
Given that all three faces are different in a throw of three dice, find the probability that
(i) at least one is a six
(ii) the sum is 9.
Solution:
Three dice are thrown once showing different faces in a throw.
|S| = 6³ = 216
Let A be the event that atleast one is a six.
Let B be the event that all three faces are different.
|B| = ⁶6₃
(i) Now A^c is the event that there is no six. A^c ∩ B is the event that all 3 faces are different and 6 does not occur.
|A^c ∩ B| = ⁵C₃
P (A^c | B) = \(\frac{P\left(A^C \cap B\right)}{P(B)}\)
= \(\frac{{ }^5 \mathrm{C}_3 / 216}{{ }^6 \mathrm{C}_3 / 216}\) = \(\frac{1}{2}\)

(ii) Let A be the event that the sum is 9.
A ∩ B = {(1,3, 5), (1,5, 3), (3, 5,1), (3, 1, 5), (5, 1, 3), (5, 3, 1), (1, 2, 6), (1, 6, 2), (2, 1, 6), (2, 6, 1), (6, 2, 1), (6, 1, 2), (2, 3, 4), (2, 4, 3), (3, 2, 4), (2, 3, 4), (3, 4, 2), (4, 3, 2)}
|A ∩ B| = 18
P (A | B) = \(\frac{P(A \cap B)}{P(B)}\)
= \(\frac{18 / 216}{20 / 216}\) = \(\frac{9}{10}\)

Question 21.
From the set of all families having three children, a family is picked at random.
(i) If the eldest child happens to be a girl, find the probability that she has two brothers.
(ii) If one child of the family is a son, find the probability that he has two sisters.
Solution:
A family is picked up at random from a set of families having 3 children.
(i) The eldest child happens to be a girl. We have to find the probability that she has two brothers. Let G denotes a girl and B denotes a boy.
∴ P(B) = \(\frac{1}{2}\), P(G) = \(\frac{1}{2}\)
P(BB | G) = P(B) × P(G) = \(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{1}{4}\)

(ii) The one child of the family is a son. We have to find the probability that he has two sisters. We have the following mutually exclusive events:
BGG, GBG, GGB.
∴ The required probability
= P(B) × P(G) × P(G) + P(G) × P(B) + P(G) + P(G) × P(G) × P(B)
= \(\frac{1}{2}\) × \(\frac{1}{2}\) × \(\frac{1}{2}\) + \(\frac{1}{2}\) × \(\frac{1}{2}\) × \(\frac{1}{2}\) + \(\frac{1}{2}\) × \(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{3}{8}\)

Question 22.
Three persons hit a target with probability \(\frac{1}{2}\), \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively. If each one shoots at the target once,
(i) find the probability that exactly one of them hits the target
(ii) if only one of them hits the target what is the probability that it was the first person?
Solution:
Three persons hit a target with probability
\(\frac{1}{2}\), \(\frac{1}{3}\) and \(\frac{1}{4}\)
Let A, B, C be the events that the 1st person, 2nd person, 3rd person hit the target respectively.

(i) As the events are independent, the probability that exactly one of them hit the target
= P(AB’C’) + P(A’BC’) + P(A’B’C)
= P(A) P(B’) P(C’) + P(A’) P(B) P(C’) + P(A’) P(B’) P(C)

(ii) Let E₁ be the event that exactly one person hits the target.
∴ P(E₁) = \(\frac{11}{24}\)
Let E₂ be the event that 1st person hits the target
∴ P(E₂) = P(A) = \(\frac{1}{2}\)
∴ E₁ ∩ E₂ = AB’C’
⇒ P(E₁ ∩ E₂)
= P(A) × P(B’) P(C’) = \(\frac{6}{24}\)
∴ P(E₂ | E₁) = \(\frac{6 / 24}{11 / 24}\) = \(\frac{6}{11}\)

Odisha State Board BSE Odisha 10th Class Life Science Notes Chapter 1 ପୋଷଣ will enable students to study smartly.

BSE Odisha Class 10 Life Science Notes Chapter 1 ପୋଷଣ

प्रश्न और अभ्यास (ପ୍ରଶ୍ନ ଔର୍ ଅଭ୍ୟାସ)

→ ଉପକ୍ରମ (Introduction) :

• ‘‘ଜୀବନ ପ୍ରକ୍ରିୟା’ର ଗୁରୁତ୍ଵପୂର୍ଣ୍ଣ ପ୍ରକ୍ରିୟା ହେଉଛି ପୋଷଣ । ଶରୀରର ଅଭିବୃଦ୍ଧି ଓ ବିଭିନ୍ନ କ୍ଷୟକ୍ଷତିର ପୂରଣ ପାଇଁ ଖାଦ୍ୟର ଆବଶ୍ୟକତା ରହିଛି ।

→ ପୋଷଣ (Nutrition) :

• ଖାଦ୍ୟରୁ ଶକ୍ତି ନିର୍ଗତ ହୋଇଥାଏ । ଆବଶ୍ୟକ ଶକ୍ତି ଜୀବର ବାହ୍ୟ ପରିବେଶରୁ ଖାଦ୍ୟ ପରିବହନ ପ୍ରକ୍ରିୟା ସମ୍ପାଦିତ ହୁଏ, ତାହାକୁ ପୋଷଣ କୁହାଯାଏ ।
• ଖାଦ୍ୟରୁ ଶକ୍ତି ନିର୍ଗତ ହୋଇଥାଏ । ଆବଶ୍ୟକ ଶକ୍ତି ଜୀବର ବାହ୍ୟ ପରିବେଶରୁ ମିଳିଥାଏ । ଯେଉଁ ପ୍ରକ୍ରିୟାଦ୍ଵାରା ଜୀବର ବାହ୍ୟ ପରିବେଶରୁ ଅନ୍ତର୍ଦ୍ଦେଶକୁ  ସରଳୀକୃତ ଖାଦ୍ୟ ପରିବହନ ପ୍ରକ୍ରିୟା ସମ୍ପାଦିତ ହୁଏ, ତାହାକୁ ପୋଷଣ କୁହାଯାଏ।
• ଶରୀରରେ ହେଉଥ‌ିବା ସମସ୍ତ ଜୈବରାସାୟନିକ ପ୍ରକ୍ରିୟା ଯୋଗୁଁ ଜୀବନର ଧାରା ଅବ୍ୟାହତ ରହିଥାଏ ।
• ଜୀବ ଶରୀରରେ ଶକ୍ତି ଆହରଣ ଓ ଉପାଦାନ ସଂଗ୍ରହ, ପୋଷଣ ମାଧ୍ୟମରେ ହୋଇଥାଏ ।
• ସବୁଜ ଉଭିଦ ଆଲୋକଶ୍ଳେଷଣ ପ୍ରକ୍ରିୟାରେ ନିଜ ଖାଦ୍ୟ ନିଜେ ପ୍ରସ୍ତୁତ କରିଥାଏ ଓ ପରିବେଶରୁ ଆବଶ୍ୟକ ପୋଷକ ମଧ୍ୟ ଗ୍ରହଣ କରିଥାଏ ।
• ପ୍ରାଣୀ ଓ ଅନ୍ୟସବୁ ଜୀବ ଖାଦ୍ୟ ପାଇଁ, ଉଭିଦ ଉପରେ ପ୍ରତ୍ୟକ୍ଷ ବା ପରୋକ୍ଷ ଭାବରେ ନିର୍ଭରଶୀଳ ଅଟନ୍ତି । ଉପାଦାନରେ ପରିଣତ ହୋଇ ସବୁ ଅଙ୍ଗ-ପ୍ରତ୍ୟଙ୍ଗରେ ଉପଲବ୍‌ଧ ହୋଇଥାଏ ।
• ସରଳ ଖାଦ୍ୟର ଦହନ ଓ ଜାରଣ ଘଟି ଶକ୍ତି ମୋଚିତ ହୋଇଥାଏ ।
• ଶକ୍ତିମୋଚନ ଏକ ତଥାକଥ୍ ଧ୍ୱଂସାତ୍ମକ ପ୍ରକ୍ରିୟା । ଏହା ‘ଅପଚୟ’ର ଉଦାହରଣ ।
• ଖାଦ୍ୟରୁ ଶରୀର ଗଠନ ପାଇଁ ଆବଶ୍ୟକ ଉପାଦାନ ସୃଷ୍ଟିହେବା ଏକ ଗଠନମୂଳକ ପ୍ରକ୍ରିୟା ଅଟେ । ଏହାକୁ ‘ଚୟ’ କୁହାଯାଏ । ଚୟ ଓ ଅପଚୟର ସମାହାର ହେଉଛି ‘ଚୟାପଚୟ’ (ଚୟାପଚୟ = ଚୟ + ଅପଚୟ) । ଏହା ଜୀବ ଶରୀରରେ ସବୁବେଳେ ଚାଲିଥାଏ ।

→ ଖାଦ୍ୟର ପ୍ରକାରଭେଦ (Types of food) :

• ରାସାୟନିକ ଗଠନ, କାର୍ଯ୍ୟ ଓ ଶକ୍ତି ପ୍ରଦାନକାରୀ ତଥା ଶରୀର ଗଠନକାରୀ କ୍ଷମତା ଉପରେ ନିର୍ଭରକରି ଖାଦ୍ୟକୁ ମୁଖ୍ୟତଃ 6 ଭାଗର ବିଭକ୍ତ କରାଯାଇଛି । ଯଥା – ଶ୍ଵେତସାର, ପୁଷ୍ଟିସାର, ସ୍ନେହସାର, ଧାତୁସାର, ଭିଟାମିନ୍ ଏବଂ ଜଳ ।

→ ଶ୍ଵେତସାର (Carbohydrates) :

• ଆମେ ଖାଉଥ‌ିବା ଖାଦ୍ୟର ପ୍ରଧାନ ଶ୍ଵେତସାର ହେଉଛି ଶର୍କରା ଓ ମଣ୍ଡଦ ।
• ଶ୍ଵେତସାରରୁ ଆମେ ସହଜରେ ଶକ୍ତି ଆହରଣ କରିଥାଉ ।
• ଗୁ କୋଜି (C₆ H₈ O₆)ରେ ରହିଛି କାର୍ବନ, ଉଦଜାନ ଏବଂ ଅମ୍ଳଜାନ ।
• କୋଷୀୟ ଶ୍ୱସନ ବେଳେ ଗ୍ଲୁକୋଜର ଜାରଣ ଫଳରେ ଅଙ୍ଗାରକାମ୍ଳ ଓ ଜଳ ସୃଷ୍ଟି ହେବା ସହିତ ଶକ୍ତି ନିର୍ଗତ ହୋଇଥାଏ ।
  CH₂O + 6O₂ → 6CO₂ + 6HO + ଶକ୍ତି
• ଏକ ଗ୍ରାମ୍ ଶ୍ଵେତସାରରୁ ପ୍ରାୟ 16 କିଲୋ ଜୁଲ (KJ) ଶକ୍ତି ନିର୍ଗତ ହୋଇଥାଏ ।

I. ଆଳୁ, ଭାତ ଓ ରୁଟିରେ ଥ‌ିବା ଶ୍ଵେତସାର ମଣ୍ଡଦ ଅଟେ ।
II. ଚିନି ଓ ଗୁଡ଼ରେ ଥ‌ିବା ଶ୍ଵେତସାର ସୁକ୍ରୋଜ ଅଟେ ।
III. ଫଳରସ ଓ ପନିପରିବାରେ ଥିବା ଶ୍ଵେତସାର ଗ୍ଲୁକୋଜ ଅଟେ ।

→ ପୁଷ୍ଟିସାର (Protein) :

• ମାଛ, ମାଂସ, ଅଣ୍ଡାର ଧଳା ଅଂଶ, ଛେନା ଓ କ୍ଷୀର ପରି ପ୍ରାଣିଜ ଦ୍ରବ୍ୟ ଓ ଡାଲି ଜାତୀୟ ଶସ୍ୟ, ସୋୟାବିନ୍ ଆଦିରୁ ଆମେ ଉଭିଦଜାତ ପୁଷ୍ଟିସାର ପାଇଥାଉ ।
• ବିଭିନ୍ନ କୋଷ ନିକଟରେ ପହଞ୍ଚାଏ । ଶରୀରର ବୃଦ୍ଧି, ନୂତନ କୋଷ ଓ ତନ୍ତୁ ଗଠନ ପାଇଁ ପୁଷ୍ଟିସାର ଏକାନ୍ତ ଆବଶ୍ୟକ ।

→ (Fats / Lipids) :

• ମାଂସ, କ୍ଷୀର, ଛେନା, ଲହୁଣୀ, ଅଣ୍ଡାର ହଳଦିଆ ଅଂଶ ଓ ତେଲ, ଘିଅରେ ସ୍ନେହସାର ଜାତୀୟ ଖାଦ୍ୟ ରହିଥାଏ । ଶରୀରରେ ସ୍ନେହସାର ଚର୍ବି ଭାବରେ
• ସଂଚିତ ହୋଇ ରହେ ଓ ଆବଶ୍ୟକ ସ୍ଥଳେ କୋଷୀୟ ଶ୍ଵାସନଦ୍ୱାରା ଏହାର ଜାରଣ ହୁଏ ଓ ଏହା ଶରୀରକୁ ଶକ୍ତି ଯୋଗାଇଥାଏ ।
• ଚର୍ମତଳେ ଚର୍ବିର ଏକ ଆସ୍ତରଣ ରହିଥାଏ ଓ ଏହା ତାପ ଅପରିବାହୀ ହୋଇଥିବାରୁ ଶରୀରକୁ ଉଷୁମ ରଖିବାରେ ସାହାଯ୍ୟ କରିଥାଏ । କୋଷଝିଲ୍ଲୀ ଗଠନ ପାଇଁ ଓ ଶକ୍ତି ପାଇଁ ଏହାର ମୁଖ୍ୟ ଭୂମିକା ରହିଛି ।

→ ଧାତୁସାର (Minerals) :

• ଶରୀର ଗଠନପାଇଁ ବିଭିନ୍ନ ଧରଣର ଧାତୁସାର ଯଥା-ଲୌହ (Fe), କ୍ୟାଲସିୟମ୍ (Ca), ଆୟୋଡ଼ିନ୍ (I), ଫସ୍‌ଫରସ୍ (P), ସୋଡ଼ିୟମ୍‌(Na), ପୋଟାସିୟମ୍ (K) ଆଦି ଆବଶ୍ୟକ ।
• ଶରୀରର ଆୟନ ସନ୍ତୁଳନ (Ionic balance) ରକ୍ଷା କରିବାରେ ଧାତୁସାରର ପ୍ରମୁଖ ଭୂମିକା ରହିଥାଏ ।

ଶରୀରରେ ଦାନ୍ତ ଓ ହାଡ଼ର ଗଠନ ପାଇଁ କ୍ୟାଲସିୟମ୍ (Ca) ଓ ଲୋହିତ ରକ୍ତ କଣିକା (RBC)ରେ ଥିବା ହିମୋଗ୍ଲୋବିନ୍‌ର ଗଠନ ପାଇଁ ଲୌହ ଆବଶ୍ୟକ ହୋଇଥାଏ ।

→ ଭିଟାମିନ୍ (Vitamins) :

• କୋଷରେ ବିଭିନ୍ନ ପ୍ରକାର ରାସାୟନିକ ପ୍ରକ୍ରିୟା ଏନଜାଇମ୍ ସାହାଯ୍ୟରେ ହୋଇଥାଏ ।
• ଭିଟାମିନ୍ ଅଭାବରୁ ଶରୀରରେ ବିଭିନ୍ନ ପ୍ରକାରର ରୋଗ ହୋଇଥାଏ ।
• ଭିଟାମିନ୍ ଅଭାବରୁ ଶରୀରରେ ବିଭିନ୍ନ ପ୍ରକାରର ରୋଗ ହୋଇଥାଏ ।

→ ଜଳ (Water):

• କୋଷରେ ଥ‌ିବା କୋଷରସ ବା କୋଷ ଜୀବକର ପ୍ରାୟ 70-୨୦ ଭାଗ ଜଳ ଅଟେ ।
• କୋଷର ସ୍ଥିତି ଓ ଏଥରେ ହେଉଥ‌ିବା ବିଭିନ୍ନ ପ୍ରକ୍ରିୟା ପାଇଁ ଜଳ ଏକାନ୍ତ ଆବଶ୍ୟକ ।
• ଝାଳ, ପରିସ୍ରା ଓ ନିଃଶ୍ବାସରେ ଶରୀରରୁ ଜଳ କ୍ଷୟ ହୋଇଥାଏ, ତାହାର ଭରଣା ପାଇଁ ପ୍ରତିଦିନ ପ୍ରାୟ 3 – 4 ଲିଟର ପାଣି ପିଇବା ଉଚିତ ।
• ଶରୀରରେ ଜଳୀୟ ଅଂଶ କମିଗଲେ ଶରୀର ଅବଶ ହୋଇଯାଏ ଓ ବିଭିନ୍ନ ଅସୁସ୍ଥତା ଦେଖାଦିଏ ।
  

→ ପୋଷଣର ପ୍ରକାରଭେଦ (Types of Nutrition) :
→ (Autotrophic nutrition):

• ଯେଉଁ ଜୀବମାନେ ନିଜ ଖାଦ୍ୟ ନିଜେ ପ୍ରସ୍ତୁତ କରିପାରନ୍ତି, ସେମାନଙ୍କୁ ସ୍ଵଭୋଜୀ କୁହାଯାଏ ।
• ପତ୍ରହରିତ୍‌ ଥ‌ିବା ସମସ୍ତ ଉଭିଦ ଓ ନୀଳ ହରିତ ଶୈବାଳ ସୁଭୋଜୀର ଉଦାହରଣ ଅଟନ୍ତି ।
• ସେମାନେ ପରିବେଶରୁ କଞ୍ଚାମାଲ ଓ ଶକ୍ତି ବ୍ୟବହାର କରି ଆବଶ୍ୟକ କରୁଥିବା ସମସ୍ତ ପ୍ରକାର ଖାଦ୍ୟ ସେମାନଙ୍କ ଟିସୁ ମଧ୍ୟରେ ପ୍ରସ୍ତୁତ କରନ୍ତି ।
• ଏମାନଙ୍କ ପୋଷଣକୁ ସ୍ବଭୋଜୀ ପୋଷଣ କୁହାଯାଏ । ଏହା ଦୁଇଟି ଉପାୟରେ ହୋଇଥାଏ । ଯଥା – ଆଲୋକଶ୍ଳେଷଣ ଓ ରସାୟଶ୍ଳେଷଣ ।

→ (Photosynthesis) :

• ସବୁଜ ଉଭିଦ ଓ ନୀଳ ହରିତ୍ ଶୈବାଳ ସୂର୍ଯ୍ୟର ଆଲୋକ ଶକ୍ତିକୁ ଉପଯୋଗ କରି ସବୁଜକଣିକାର ଉପସ୍ଥିତିରେ ଅଙ୍ଗାରକାମ୍ଳ ଓ ଜଳ ମଧ୍ୟରେ ସଂଯୋଗ ଘଟାଇ ଶ୍ଵେତସାର ଜାତୀୟ ଖାଦ୍ୟ ପ୍ରସ୍ତୁତ କରିଥା’ନ୍ତି । ଏହି ପ୍ରକ୍ରିୟାକୁ ଆଲୋକଶ୍ଳେଷଣ କୁହାଯାଏ ।
  

→ (Chemosynthesis):
ନାଇଟ୍ରେଟ୍ ପ୍ରସ୍ତୁତକାରୀ ବ୍ୟାକ୍ଟେରିଆ ଓ ଗନ୍ଧକ ବ୍ୟାକ୍ଟେରିଆ ପରି କେତେକ ରସାୟଶ୍ଳେଷଣ ବ୍ୟାକ୍ଟେରିଆ ଏକ ବିଶେଷ ଅଜୈବ ରାସାୟନିକ ପ୍ରକ୍ରିୟାରୁ ମିଳୁଥିବା ରାସାୟନିକ ଶକ୍ତି ସଂଗ୍ରହ କରିଥା’ନ୍ତି । ଏହି ପ୍ରକ୍ରିୟାକୁ ରସାୟଶ୍ଳେଷଣ କୁହାଯାଏ ।

→ (Heterotrophic Nutrition) :

• ଯେଉଁ ଜୀବମାନେ ନିଜ ଖାଦ୍ୟ ନିଜେ ପ୍ରସ୍ତୁତ କରିନପାରି ପୋଷଣ ପାଇଁ ଅନ୍ୟ ପ୍ରାଣୀ ବା ଉଭିଦ ଉପରେ ନିର୍ଭର କରନ୍ତି ସେମାନଙ୍କୁ ପରଭୋଜୀ କୁହାଯାଏ।
• ସମସ୍ତ ପ୍ରାଣୀ, ମଲାଙ୍ଗ, ନିର୍ମୂଳୀ, ରାଫ୍ଲେସିଆ ଆଦି ପରଜୀବୀ ଉଭିଦ, କବକ ଏବଂ ଅଧିକାଂଶ ବ୍ୟାକ୍ଟେରିଆ ପରଭୋଜୀ
• ଏହି ଜୀବମାନଙ୍କ ପୋଷଣ ପ୍ରଣାଳୀକୁ ପରଭୋଜୀ ପୋଷଣ କୁହାଯାଏ ।

→ ପରଭୋଜୀ ପୋଷଣର ପ୍ରକାରଭେଦ :
ପରଭୋଜୀ ପୋଷଣ ମୁଖ୍ୟତଃ ଚାରିପ୍ରକାର ।

(i) (Holozoic nutrition) :

• ପରଜୀବୀୟ ପ୍ରାଣୀଙ୍କୁ ଛାଡ଼ି ଅନ୍ୟ ସମସ୍ତ ପ୍ରାଣୀ ଏହି ପ୍ରଣାଳୀରେ ଅନ୍ୟ ଉଦ୍ଭଦ ବା ପ୍ରାଣୀଙ୍କୁ ସଂପୂର୍ଣ୍ଣ ଅଥବା ଆଂଶିକ ଭାବରେ ଖାଦ୍ୟରୂପେ ଗ୍ରହଣ କରିଥା’ନ୍ତି ।
• ପରିପାକ ପରେ ସରଳୀକୃତ ଖାଦ୍ୟର ଆତ୍ମୀକରଣ ବା ଅନ୍ତର୍ଗହଣ ହୋଇଥାଏ ।
• ଏହା ଶରୀର ଗଠନରେ ଓ ଶରୀରକୁ କାର୍ଯ୍ୟକ୍ଷମ ରଖିବାରେ ସହାୟକ ହୋଇଥାଏ ।

(ii) ମୃତୋପଜୀବୀୟ ପୋଷଣ (Saprophytic nutrition) :

• ଯେଉଁ ପରଭୋଜୀ, ମୃତ, ଗଳିତ, ପଚାସଢ଼ା ଉଭିଦ ବା ପ୍ରାଣୀରୁ ଖାଦ୍ୟ ସଂଗ୍ରହ କରି ନିଜ ପୁଷ୍ଟିସାଧନ କରିଥା’ନ୍ତି ସେମାନଙ୍କୁ ମୃତୋପଜୀବୀ କୁହାଯାଏ ।
• ଏହି ଜୀବମାନେ କଠିନ ପଦାର୍ଥକୁ ଖାଦ୍ୟରୂପେ ଗ୍ରହଣ କରିପାରନ୍ତି ନାହିଁ ।
• ସାଧାରଣତଃ ଖାଦ୍ୟ ଗ୍ରହଣବେଳେ ଏମାନେ ନିଜ ଶରୀରରୁ ପାଚକ ରସ କ୍ଷରଣ କରି, ଶରୀର ବାହାରେ ହିଁ ଜଟିଳ ଖାଦ୍ୟକୁ ସରଳ ଖାଦ୍ୟରେ ପରିଣତ କରି ଓ ପରେ ସରଳୀକୃତ ଖାଦ୍ୟକୁ ଶରୀର ମଧ୍ୟକୁ ଶୋଷଣ କରି ଶରୀର ଗଠନରେ
• ଛତୁ ଜାତୀୟ କବକ, ଇଷ୍ଟ୍, ବ୍ୟାକ୍ଟେରିଆ ଆଦି ଜୀବମାନଙ୍କଠାରେ ଏହିପରି ପୋଷଣ ଦେଖିବାକୁ ମିଳିଥାଏ ।

(iii) (Parasitic Nutrition) :

• ଯେଉଁ ଜୀବମାନେ ଅନ୍ୟ ଜୀବନ୍ତ ଉଭିଦ ବା ପ୍ରାଣୀଙ୍କ ଶରୀର ଭିତରେ ବା ବାହାରେ ରହି ସେମାନଙ୍କଠାରୁ ଖାଦ୍ୟ ସଂଗ୍ରହ କରି ନିଜର ପୁଷ୍ଟିସାଧନ କରନ୍ତି ସେମାନଙ୍କୁ ପରଜୀବୀ କୁହାଯାଏ ।
• ପରଜୀବୀମାନେ ଭୋଜଦାତା ଉଭିଦ ବା ପ୍ରାଣୀଙ୍କଠାରୁ ସରଳୀକୃତ ଖାଦ୍ୟ ସିଧାସଳଖ ଗ୍ରହଣ କରି ନିଜର ପୁଷ୍ଟିସାଧନ କରିଥା’ନ୍ତି ।
• ଭୋଜଦାତାର ଆଶ୍ରୟରେ ରହି ପରଜୀବୀମାନେ ସାଧାରଣତଃ ତାହାର ଅନିଷ୍ଟ କରିଥା’ନ୍ତି ।
• ମଲାଙ୍ଗ, ନିର୍ମୂଳୀ, ରାଫ୍ଲେସିଆ ଆଦି ଉଭିଦ, ପ୍ଲାସ୍‌ଡ଼ିୟମ୍, ଉକୁଣୀ, ଜୋକ, କେତେକ କୃମି ପରି ପ୍ରାଣୀ ପରଜୀବୀ

କେତେକ ଭୋଜଦାତାର ଶରୀର ଭିତରେ ଅନ୍ତଃପରଜୀବୀ ଭାବେ ( ଉଦାହରଣ- ପ୍ଲାସ୍‌ମୋଡ଼ିୟମ୍) ଓ କେତେକ ଶରୀର ବାହାରେ ବାହ୍ୟପରଜୀବୀ ଭାବେ ( ଉଦାହରଣ – ଉକୁଣୀ) ରହିଥା’ନ୍ତି ।

(iv) (Symbiotic Nutrition) :

• ବେଳେବେଳେ ଦୁଇଟି ସଂପୂର୍ଣ୍ଣ ଭିନ୍ନ ଜାତିର ପ୍ରାଣୀ, ଅଥବା ଉଭିଦ ଓ ପ୍ରାଣୀ ବା ପ୍ରାଣୀ ଓ ଅଣୁଜୀବ ବା ଉଭିଦ ଓ ଅଣୁଜୀବ ଏକାଠି ବାସ କରୁଥିବା ଦେଖାଯାଏ । ଏହାକୁ ସହଜୀବୀତା କୁହାଯାଏ ।
• ଏଥୁରେ କେହି କାହାରି କ୍ଷତି କରନ୍ତି ନାହିଁ, ବରଂ ସେମାନଙ୍କ ଭିତରେ ପୋଷଣର ଆଦାନ ପ୍ରଦାନ ମଧ୍ୟ ହୋଇଥାଏ । ଏହାକୁ ସହଜୀବୀୟ ପୋଷଣ କୁହାଯାଏ।
• ଆମ ଅନ୍ତନଳୀରେ ସହଜୀବୀଭାବେ ରହୁଥ‌ିବା ଇସ୍‌ରିଚିଆ କୋଲାଇ ନାମକ ବ୍ୟାକ୍ଟେରିଆ ନିଜ ଶରୀରରେ ଭିଟାମିନ୍ (B₁₂) (ସାୟନୋକୋବାଲାମିନ୍) ପ୍ରସ୍ତୁତ କରି ଆମକୁ ଯୋଗାଇଥାଏ । ତା’ ପରିବର୍ତ୍ତେ ଆମ ଅନ୍ତନଳୀର ସରଳୀକୃତ ଖାଦ୍ୟଗ୍ରହଣ କରି ନିଜର ପ୍ରତିପାଳନ କରିଥାଏ ।
• 

→ ଖାଦ୍ୟାଭାସକୁ ଆଧାର କରି ମୁଖ୍ୟତଃ ତିନି ଜାତିର ପ୍ରାଣୀ ଅଛନ୍ତି ।
(a) ଶାକାହାରୀ – ଉଭିଦ ବା ଉଭିଦଜାତ ପଦାର୍ଥ ଭକ୍ଷଣ କରୁଥିବା ପ୍ରାଣୀ ।
(b) ମାଂସାହାରୀ – ଅନ୍ୟ ପ୍ରାଣୀ ବା ପ୍ରାଣିଜ ପଦାର୍ଥକୁ ଭକ୍ଷଣ କରୁଥିବା ପ୍ରାଣୀ ।
(c) ସର୍ବାହାରୀ – ଖାଦ୍ୟରେ ବାଛବିଚାର ନ କରି ଯାହା ଖାଦ୍ୟୋପଯୋଗୀ ତାହା ଭକ୍ଷଣ କରୁଥିବା ପ୍ରାଣୀ । ଆଲୋକଶ୍ଳେଷଣ

→ (Photosynthesis) :

• ସବୁଜ ଉଭିଦ ଆଲୋକଶ୍ଳେଷଣ ପ୍ରକ୍ରିୟାରେ ଶ୍ଵେତସାର ଜାତୀୟ ଖାଦ୍ୟ ପ୍ରସ୍ତୁତ କରିଥା’ନ୍ତି । ଏହି ଶ୍ଵେତସାର ଜାତୀୟ ଖାଦ୍ୟ ଜୀବଜଗତର ସବୁ ଜୀବଙ୍କ ପାଇଁ ପ୍ରତ୍ୟକ୍ଷ ବା ପରୋକ୍ଷ ଖାଦ୍ୟ ଅଟେ ।
• ଯେଉଁ ପ୍ରକ୍ରିୟାଦ୍ଵାରା ସବୁଜ ଉଭିଦ ସବୁଜକଣା ବା କ୍ଲୋରୋଫିଲ୍ ମାଧ୍ୟମରେ ଦୃଶ୍ୟମାନ ଆଲୋକ ଶକ୍ତିକୁ ରାସାୟନିକ ଶକ୍ତିରେ ରୂପାନ୍ତରିତ କରିବା ସହିତ ପରିବେଶରୁ ଗ୍ରହଣ କରିଥିବା ଅଙ୍ଗାରକାମ୍ଳ ଓ ଜଳକୁ ଉପଯୋଗ କରି ସରଳ ଶର୍କରା ତିଆରି କରିଥାଏ, ତାହା ଆଲୋକଶ୍ଳେଷଣ ପ୍ରକ୍ରିୟା ଅଟେ ।

→ ଆଧାର ଓ ସଂସ୍ଥା:

• ପ୍ରତ୍ୟେକ ପ୍ରକ୍ରିୟା ପାଇଁ ଏକ ଆଧାର ଓ ସଂସ୍ଥା ଆବଶ୍ୟକ ହୋଇଥାଏ ।
• ସବୁଜ ଉଦ୍ଭଦରେ ଆଲୋକଶ୍ଳେଷଣ ପାଇଁ ବ୍ୟବହୃତ ଆଧାର ସବୁଜ ପତ୍ର ଅଟେ । ସବୁଜ ପତ୍ରର ପୃଷ୍ଠରେ ଥ‌ିବା ଛୋଟ ଛୋଟ ରନ୍ଧ୍ରଗୁଡ଼ିକୁ ସ୍ତୋମ୍ ବା ଷ୍ଟୋମାଟା କୁହାଯାଏ । ଏହି ସ୍ତୋମ୍ ଦେଇ ପରିବେଶ ଓ ପତ୍ର ମଧ୍ୟରେ ଅଙ୍ଗାରକାମ୍ଳ ଓ ଜଳୀୟବାଷ୍ପର ବିନିମୟ ଘଟେ । ସବୁଜପତ୍ରର ଅନ୍ତଃଗଠନ ସବୁଜ ରଙ୍ଗଯୁକ୍ତ ପାଲିସେଡ଼୍ ଓ ସ୍ପଞ୍ଜି ପାରେନ୍‌କାଇମା ଟିସୁଦ୍ୱାରା ହୋଇଥାଏ । ପତ୍ର ଭିତରେ ଥ‌ିବା ଏହି ଦୁଇ ପ୍ରକାର ପାରେନ୍‌କାଇମା ଟିସୁର କୋଷ ଭିତରେ କ୍ଲୋରୋପ୍ଲାଷ୍ଟ ନାମକ ଅଙ୍ଗିକା ରହିଥାଏ । କ୍ଲୋରୋପ୍ଲାଷ୍ଟରେ ଥ‌ିବା ରସକୁ ବ୍ୟୋମା କୁହାଯାଏ ।
• ଥାଇଲାକଏଡ଼ ଦୀର୍ଘ ସରୁ ଚେପଟା ଥଳି ସଦୃଶ । ଥଳିର ଭିତର ସ୍ଥାନକୁ ମ୍ୟୁମେନ କୁହାଯାଏ । କେତେକ ସ୍ଥାନରେ ଛୋଟ ଥାଇଲାକଏଡ଼ ଥାକ ଥାକ ହୋଇ ସଜ୍ଜିତ ହୋଇ ରହିଥା’ନ୍ତି । ଏଭଳି ଥାକକୁ ଗ୍ରାନା କୁହାଯାଏ ।

→ ଆଧାର :
1. ସବୁଜ ପତ୍ରରେ ଥ‌ିବା ସ୍ତୋମ
2. ସବୁଜ ରଙ୍ଗଯୁକ୍ତ ପାଲିସେଡ଼ ଓ ସ୍ପଞ୍ଜି ପାରେନ୍‌କାଇମା ।
3. କ୍ଲୋରୋପ୍ଲାଷ୍ଟ

→ କ୍ଲୋରୋପ୍ଲାଷ୍ଟ :

• ବ୍ୟୋମା (ରସ)ରେ ଏନ୍‌ଜାଇମ୍ ଥାଏ ।
• ଦ୍ୱସ୍ତରୀୟ ଥାଇଲାକଏଡ୍.
• ଭିତର ଙ୍ଗାନ ଲୁମେନ୍‌
• ଥାକକୁ ଗ୍ରାନା କହନ୍ତି ।

ଥାଇଲାକଏଡ଼ର ପ୍ରତ୍ୟେକ ଝିଲ୍ଲୀ ସ୍ତରରେ କ୍ଲୋରୋଫିଲ୍, ପ୍ରୋଟିନ୍ ଓ ଲିପିଡ଼ର ବିଭିନ୍ନ ବୃହତ୍ ଅଣୁ ସଜେଇ ହୋଇ ରହିଥା’ନ୍ତି । ଏହିଭଳି ଗଠନଯୁକ୍ତ ଥାଇଲାକଏଡ଼ ଓ କ୍ଲୋରୋପ୍ଲାଷ୍ଟର ଷ୍ଟ୍ରୋମା ରସ ‘ଆଲୋକଶ୍ଳେଷଣ ସଂସ୍ଥା’ ସୃଷ୍ଟି କରିଥା’ନ୍ତି ।

→ ପ୍ରକ୍ରିୟା :

• ଆଲୋକଶ୍ଳେଷଣ ପ୍ରକ୍ରିୟାକୁ ଜାଣିବାପାଇଁ ବିଭିନ୍ନ ପରୀକ୍ଷା କରାଯାଇଛି ।
• ପ୍ରଥମ ସିଦ୍ଧାନ୍ତ 1905 ମସିହାରେ ଫ୍ରେଡ଼ରିକ୍ ବ୍ଲାକ୍‌ମ୍ୟାନ୍ (Frederick Blackman) ଜଣାଇଥିଲେ ।
• ଗୋଟିଏ ସହ ପ୍ରକ୍ରିୟା ଦୃଶ୍ୟମାନ ଆଲୋକ ଉପରେ ନିର୍ଭର କରେ । ଏହାକୁ ଆଲୋକ ପ୍ରକ୍ରିୟା କୁହାଯାଏ । ଅନ୍ୟଟି ଆଲୋକ ଉପରେ ନିର୍ଭର କରିନଥାଏ । ଏହାକୁ ଅନ୍ଧକାର ପ୍ରକ୍ରିୟା କୁହାଯାଏ ।

• ଆସୁଥ‌ିବା ହାଇଡ୍ରୋଜେନ୍‌ଦ୍ୱାରା ଅଙ୍ଗାରକାମ୍ଳ ବିଜାରିତ ହୁଏ ଓ ସରଳ ଶର୍କରା ସଂଶ୍ଳେଷିତ ହେବା ସହିତ ଅମ୍ଳଜାନ ନିର୍ଗତ ହେବା ଦର୍ଶାଯାଇଥିଲା । ଏହା 1931 ମସିହରେ ଫନ୍‌ ନିଲ୍‌ଙ୍କଦ୍ବାରା ପରିକଳ୍ପନା କରାଯାଇଥିଲା । ରବର୍ଟ ହିଲ୍ 1937 ମସିହାରେ ଉନ୍ନତମାନର ପରୀକ୍ଷଣ ମାଧ୍ୟମରେ ପରିକଳ୍ପନାଟିକୁ ପ୍ରମାଣିତ କରିଥିଲେ । କ୍ଲୋରୋପ୍ଲାଷ୍ଟ କ୍ଲୋରୋଫିଲ୍ ମାଧ୍ୟମରେ ଆଲୋକ ଶକ୍ତିକୁ ବ୍ୟବହାର କରି ଗ୍ଲୁକୋଜ ସଂଶ୍ଳେଷଣ କରିଥାଏ । ଏହା ପାଇଁ 6 ଟି ଅଙ୍ଗାରକାମ୍ଳ (CO₂) ଓ 12 ଟି ଜଳ (H₂O) ଅଣୁ ବ୍ୟବହୃତ ହୁଏ ।

→ ଆଲୋକ ପ୍ରକ୍ରିୟା

• ଆଲୋକ ପ୍ରକ୍ରିୟା ଦୃଶ୍ୟମାନ ଆଲୋକ ଉପସ୍ଥିତିରେ ଥାଇଲାକଏଡ୍ ଝିଲ୍ଲୀରେ ସଂଗଠିତ ହୁଏ ।
• ପ୍ରଥମ ପର୍ଯ୍ୟାୟରେ ଝିଲ୍ଲୀରେ ସଜ୍ଜିତ କ୍ଲୋରୋଫିଲ୍ ଅଣୁଗୁଡ଼ିକର ସମଷ୍ଟି ଆଲୋକ ଶକ୍ତି ଗ୍ରହଣ କରନ୍ତି ।
• ପର୍ଯ୍ୟାୟକ୍ରମେ ଅନ୍ୟାନ୍ୟ କ୍ଲୋରୋଫିଲକୁ ଶକ୍ତି ସ୍ଥାନାନ୍ତରିତ କରିଥା’ନ୍ତି ।
• କ୍ଲୋରୋଫିଲ୍‌କୁ ଆଲୋକ ପ୍ରତିକ୍ରିୟା କେନ୍ଦ୍ର ବା Photosystem I କୁ P700 କୁହାଯାଏ ।
• କ୍ଲୋରୋଫିଲ୍‌ରୁ ଅଧ‌ିକ ଶକ୍ତି ସମ୍ପନ୍ନ ଅସ୍ଥିର ଇଲେକଟ୍ରନ୍ ବାହାରି ଆସେ ।
• ଇଲେକ୍ସନ୍ ବିଭିନ୍ନ ବାହକ ଅଣୁ ମାଧ୍ୟମରେ ଗତିକରି ଏକ ଗ୍ରାହକ ଅଣୁ ପାଖରେ ପହଞ୍ଚେ ।
• ଶେଷ ଗ୍ରାହକ ଅଣୁକୁ ସହକାରକ କୁହାଯାଏ ।
• ନିକୋଟିନାମାଇଡ୍ ଏଡ଼େନାଇନନ୍ ଡାଇନ୍ୟୁକ୍ଲିଟାଇଡ଼ ଫସ୍‌ଫେଟ୍ ବା NADP⁺ ଇଲେକଟ୍ରନ୍ ଗ୍ରହଣ କରି ବିଜାରିତ NADPH ରେ ପରିଣତ ହୁଏ ।
  ଦ୍ୱିତୀୟ ପର୍ଯ୍ୟାୟରେ ଇଲେକ୍ସନ୍ ଶୂନ୍ୟତାକୁ ପୂରଣ କରିବାପାଇଁ ଆଲୋକ ପ୍ରତିକ୍ରିୟା କେନ୍ଦ୍ର P680 ବା Photosystem II କେନ୍ଦ୍ରରୁ ଇଲେକଟ୍ରନ୍ ଆସିଥାଏ ।
• ଏହାଦ୍ଵାରା ଥାଇଲାକଏଡ ପରିବେଶରେ ଜଳ ଅଣୁର ଆଲୋକ ବିଶ୍ଳେଷଣ ହୁଏ । ଫଳରେ e^–, H⁺, Q, ନିର୍ଗତ ହୁଏ ।
• ଥାଇଲାକଏଡ ମଧ୍ଯସ୍ଥିତ ଲ୍ୟୁମେନରେ ପ୍ରୋଟନ ଜମା ହୁଏ ।
• ଏହାଦ୍ୱାରା ସୃଷ୍ଟ ଅବକ୍ରମ ବଳକୁ ଉପଯୋଗ କରି ADP ଅଧ‌ିକ ଶକ୍ତି ସମ୍ପନ୍ନ ATP ରେ ପରିଣତ ହୁଏ ।
• NADPH ଓ ATP ଉଭୟ ମିଶି ଆଲୋକଶ୍ଳେଷଣ ଶକ୍ତି ଗଠନ କରନ୍ତି ।

→ ଅନ୍ଧକାର ପ୍ରକ୍ରିୟା

• ଆଲୋକ ଉପରେ ଅନ୍ଧକାର ପ୍ରକ୍ରିୟା ନିର୍ଭର କରିନଥାଏ ।
• ଅଙ୍ଗାରକାମ୍ଳ ସ୍ତୋମ୍ ଦେଇ ଷ୍ଟୋମାରସରେ ଦ୍ରବୀଭୂତ ହୁଏ ।
• ବ୍ୟୋମା ରସରେ 5-କାର୍ବନ ଯୁକ୍ତ ଏକ ଗ୍ରାହକ ଅଣୁ ଆଲୋକଶ୍ଳେଷଣ ଶକ୍ତି ବ୍ୟବହାର କରି ଏନ୍‌ଜାଇମ୍ ମାଧ୍ୟମରେ ବିବନ୍ଧିତ କରାଏ । ଜୈବିକ କ୍ରିୟା ଦ୍ବାରା 3-କାର୍ବନ ଯୁକ୍ତ ଶର୍କରା ତିଆରି ହୁଏ ।
• ଗ୍ରାହନ ଅଣୁକୁ ରାଇବୋଲୋଜ୍ ବିସ୍‌ଫସ୍‌ଫେଟ୍ ବା RUBP ଓ ଏନ୍‌ଜାଇମ୍କୁ ରାଇବୋଲୋଜ୍ ବିସ୍‌ଫସଫେଟ୍ ରୁବିସ୍କୋ କୁହାଯାଏ ।
• ରୁବିସ୍କୋର ଭୂମିକା ଗୁରୁତ୍ବପୂର୍ଣ୍ଣ ।

• ଏହି ଅନ୍ଧକାର ପ୍ରକ୍ରିୟାକୁ ମେଲଭିନ୍ କେଲଭିନ୍‌ଙ୍କ ନାମାନୁସାରେ କେଲଭିନ୍‌ ଚକ୍ର କୁହାଯାଏ ।
• ପ୍ରଥମ ପର୍ଯ୍ୟାୟରେ ଗ୍ରାହକ ଅଣୁ ସହ ଅଙ୍ଗାରକାମ୍ଳର ବିବନ୍ଧନ ହୁଏ ।
• ଦ୍ଵିତୀୟ ପର୍ଯ୍ୟାୟରେ ଗ୍ଲୁକୋଜର ସଂଶ୍ଳେଷଣ ହୁଏ ।
• ତୃତୀୟ ପର୍ଯ୍ୟାୟରେ ଗ୍ରାହକ ଅଣୁର ପୁନରୁତ୍ପାଦନ ହୁଏ ।

→ (Digestive System of Man)

• ଆମେ ଖାଉଥ‌ିବା ଖାଦ୍ୟ ସମୂହ ସିଧାସଳଖ ଖାଦ୍ୟରେ ପରିଣତ ହୁଏ ଓ ଶେଷରେ ରକ୍ତରେ ମିଶି ଥାଏ । ଏହାକୁ ହଜମ (ପରିପାକ) ବା ଜୀର୍ଣ୍ଣ ହେବା କହିଥାଉ । ଅଦରକାରୀ ଅଂଶ ମଳ ରୂପେ ଶରୀରରୁ ନିଷ୍କାସିତ ହୋଇଥାଏ । ଆମର ପାକତନ୍ତ୍ର ପାକନଳୀ ଓ ପାକଗ୍ରନ୍ଥିକୁ ନେଇ ଗଠିତ ।

→ (Alimentary Canal)

• ପାକନଳୀ ପାଟିରୁ ଆରମ୍ଭ ହୋଇ ମଳଦ୍ଵାରରେ ଶେଷ ହୋଇଥାଏ ।
• ପାକନଳୀର ଗଠନ ଓ କାର୍ଯ୍ୟ ଉପରେ ନିର୍ଭର କରି ଏହାକୁ ବିଭିନ୍ନ ଅଂଶରେ ଭାଗ ଗ୍ରସନୀ, ନିଗଳ ବା ଗ୍ରାସନଳୀ, ପାକସ୍ଥଳୀ, କ୍ଷୁଦ୍ରାନ୍ତ୍ର, ବୃହଦନ୍ତ୍ର, ମଳାଶୟ ଓ ମଳଦ୍ଵାର ।

ପାକନଳୀ ଦେଖିବାକୁ ଗୋଟିଏ ଲମ୍ବ ଟ୍ୟୁବ୍ ପରି । ଏହାର କାନ୍ଥ ବର୍ତ୍ତୁଳ ବା ଚକ୍ରାକୃତି ପେଶୀ ଓ ଲମ୍ବ ଭାବରେ ବିସ୍ତୃତ ବା ଅନୁଦୈର୍ଘ୍ୟ ପେଶୀଦ୍ଵାରା ଗଠିତ ହୋଇଥାଏ । ଏହି ଦୁଇ ପ୍ରକାର ପେଶୀର ସଂକୋଚନ ଓ ଶିଳନ ଫଳରେ କୁହାଯାଏ ।

(i) ପାଟି (Mouth) :

• ଏହା ଚଳନଶୀଳ ଓଠଦ୍ୱାରା ପରିବେଷ୍ଟିତ ।
• ଏହା ଖାଦ୍ୟର ଅନ୍ତର୍ଗହଣ ପାଇଁ ଉଦ୍ଦିଷ୍ଟ ।
• ଏହା ମୁଖଗହ୍ଵରକୁ ଖୋଲି ରହିଛି ।

(ii) ମୁଖଗହ୍ଵର (Buccal Cavity) :

• ପାଟି ଭିତରକୁ ରହିଥାଏ ମୁଖଗହ୍ଵର ।
• ମୁଖଗହ୍ଵରର ଦୁଇ ପଟେ ଗାଲ; ଉପରେ ତାଳୁ ଓ
• ତଳେ ଜିଭ ରହିଥାଏ ।

(a) ଦାନ୍ତ (Tooth):

• ଉଠେ ଓ ଛଅ ବର୍ଷ ବେଳକୁ ଉକ୍ତ ଦାନ୍ତ ଝଡ଼ିବାକୁ ଆରମ୍ଭ କରେ । ଏହି ସ୍ଥାନରେ ସ୍ଥାୟୀ ଦାନ୍ତ ଉଠେ । ବୟସ୍କ ଲୋକର ତଳ ଓ ଉପର ମାଢ଼ିରେ 32ଟି (16ଟି ଲେଖାଏଁ) ଦାନ୍ତ ଥାଏ । ପ୍ରତି ମାଢ଼ିରେ 4ଟି କର୍ଜନ ଦାନ୍ତ, 2 ଟି ଛେଦକ ବା ଶ୍ଵାନଦାନ୍ତ Canine), 4 ଟି ଚର୍ବଣ ଦାନ୍ତ ଓ ଟି ପେଷଣ ଦାନ୍ତ ରହିଅଛି।
• ଖାଦ୍ୟାଭ୍ୟାସ ଉପରେ ନିର୍ଭର କରି ଆମର ଦାନ୍ତ 4 ପ୍ରକାରର ହୋଇଥାଏ ।

(b) && (Tongue) :

• ମୁଖଗହ୍ଵରର ଉପରେ ତାଳୁ ଓ ତଳେ ମୋଟା, ମାଂସଳ ଜିଭ ରହିଥାଏ । ଏଥ‌ିରେ ତିନି ପ୍ରକାର ସ୍ବାଦମୁକୂଳ ରହିଥାଏ ।

କାର୍ଯ୍ୟ :

• ଚର୍ବଣବେଳେ ଏହା ଖାଦ୍ୟକୁ ଦାନ୍ତ ନିକଟରେ ପହଞ୍ଚାଇଥାଏ ।
• ଏହା ଖାଦ୍ୟକୁ ଲାଳ ସହିତ ମିଶାଇଥାଏ ।
• ଖାଦ୍ୟକୁ ଗିଳିବାରେ ସହାୟତା କରିଥାଏ ।
• ଏହା ମିଠା, ଖଟା, ପିତା ଓ ଲୁଣିଆ ଆଦି ସ୍ଵାଦ ବାରିଥାଏ ।
• ଏହା କଥା କହିବାରେ ସହାୟତା କରିଥାଏ ।

(iii) (Pharynx and Oesophagus) :

• ନାସାପଥ ଓ ମୁଖଗହ୍ଵର ମିଶି ଗ୍ରସନୀ ତିଆରି ହୋଇଛି । ଏହା ଉଭୟ ଖାଦ୍ୟ ଓ ଶ୍ୱାସ ବାୟୁ ଯିବାପାଇଁ ଏକ ସାଧାରଣ ପଥ ।
• ଏହାର ଶେଷମୁଣ୍ଡରେ ଦୁଇଟି ଦ୍ଵାର ରହିଛି । ଗୋଟିଏ ଦ୍ଵାର ଖୋଲିଛି ଶ୍ଵାସନଳୀ ଭିତରକୁ, ଅନ୍ୟଟି ଖୋଲିଛି ଖାଦ୍ୟନଳୀ ମଧ୍ୟକୁ ।
• ଖାଦ୍ୟନଳୀର ଦ୍ଵାରକୁ ଗଲେଟ୍ ଓ ଶ୍ଵାସନଳୀର ଦ୍ଵାରକୁ ଗ୍ଲଟିସ୍ କୁହାଯାଏ । ଶ୍ଵାସନଳୀର ଦ୍ଵାରରେ ଏକ ତରୁଣାସ୍ଥିର ପ୍ଲେଟ ରହିଛି । ଏହି ପ୍ଲେଟ୍‌କୁ ଅଧ୍ୱଜିହ୍ଵା ବା ଏପିକ୍ଲଟିସ୍ କୁହାଯାଏ ।
• ପ୍ରବେଶ କରିଥାଏ ।
• ଗ୍ରାସନଳୀ ବେକ ମଧ୍ୟ ଦେଇ ତଳ ଆଡ଼କୁ ଗତି କରିଛି ଏବଂ ମଧ୍ୟଚ୍ଛଦାକୁ ଭେଦ କରି ପାକସ୍ଥଳୀକୁ ଖୋଲିଛି ।
• କାର୍ଯ୍ୟ : ଏହା ମଧ୍ୟଦେଇ ପେରିଷ୍ଟାଲ୍‌ସିସ୍‌ରା ଖାଦ୍ୟ ଆପେ ଆପେ ପାକସ୍ଥଳୀ ମଧ୍ୟକୁ ପ୍ରବେଶ କରେ । ଏଠାରେ ଖାଦ୍ୟର କୌଣସି ପରିବର୍ତ୍ତନ ହୁଏ ନାହିଁ ।

(iv) (Stomach) :

• ଏହା ମୋଟା, ମାଂସଳ ଓ ‘J’ ଆକୃତିର ଏକ ଥଳୀ ଅଟେ ଏବଂ ଏହା ଉଦର ଗହ୍ଵରର ଉପର ଅଂଶର ବାମପଟେ ରହିଥାଏ ।
• ଏହାର ଉପର ଅଂଶ ଚଉଡ଼ା ଓ ତଳ ଅଂଶ କମ୍ ଓସାରିଆ ।
• ଏହାର ଉପର ଅଂଶ ହୃତ୍‌ପିଣ୍ଡ ନିକଟରେ ଥ‌ିବାରୁ ସେହି ଅଂଶକୁ କାର୍ଡିଆକ୍ ଷ୍ଟୋମାକ୍ ଓ ତଳ ଅଂଶକୁ ପାଇଲୋରିକ୍ ଷ୍ଟୋମାକ୍ କୁହାଯାଏ ।
• ଏହାର ମାଂସଳ କାନ୍ଥ ଖାଦ୍ୟକୁ ପାଚକରସ ସହିତ ମିଶିବାରେ ସାହାଯ୍ୟ କରେ ।
• ଅର୍ଦ୍ଧଜୀର୍ଣ୍ଣ ଖାଦ୍ୟ ଅଳ୍ପ ଅଳ୍ପ ପରିମାଣରେ କ୍ଷୁଦ୍ରାନ୍ତ ମଧ୍ୟକୁ ପ୍ରବେଶ କରେ ।

(v) (Small Intestine) :

• ଏହା ପ୍ରାୟ 6 ମିଟର ଦୀର୍ଘ, ସରୁ ଓ କୁଣ୍ଡଳାକାର ନଳୀ ଅଟେ ।
• ଏହାର ପ୍ରଥମ ଅଂଶକୁ ଗ୍ରହଣୀ, ମଧ୍ୟବର୍ତୀ ଅଂଶକୁ ଯେଯୁନମ୍ ଓ ଶେଷ ଅଂଶକୁ ଇଲିୟମ୍ କୁହାଯାଏ ।
• କାର୍ଯ୍ୟ : ଏଠାରେ ପରିପାକ କ୍ରିୟା ସମ୍ପୂର୍ଣ୍ଣ ହୋଇଥାଏ ଏବଂ ପରିପାକ ହୋଇଥ‌ିବା ଖାଦ୍ୟର ଅବଶୋଷଣ ବା ଆତ୍ମୀକରଣ ଘଟିଥାଏ ।

(vi) (Large Intestine) :

• ଏହା କ୍ଷୁଦ୍ରାନ୍ତଠାରୁ ଛୋଟ ଓ ପ୍ରଶସ୍ତ ଅଟେ ।
• ଏହା ସିକମ୍, କୋଲନ୍ ଓ ମଳାଶୟ ରେ ବିଭକ୍ତ ହୋଇଥାଏ ।
• କାର୍ଯ୍ୟ : ଏଠାରେ ଅଜୀର୍ଣ୍ଣ ଖାଦ୍ୟ ମଳରେ ପରିଣତ ହୋଇଥାଏ ।

(vii)

• ଏହା ବୃହଦନ୍ତ୍ରର ଶେଷ ଆଡ଼କୁ ଅବସ୍ଥିତ ଏବଂ ଏହାର ଶେଷ ଭାଗରେ ଥ‌ିବା ଛିଦ୍ରକୁ ମଳଦ୍ଵାର କୁହାଯାଏ ।
• କାର୍ଯ୍ୟ : ମଳାଶୟରେ ମଳ କିଛି ସମୟ ପାଇଁ ଗଚ୍ଛିତ ରହେ ଏବଂ ମଳଦ୍ଵାର ଦେଇ ନିଷ୍କାସିତ ହୁଏ ।

→ ପାକଗ୍ରନ୍ଥି (Digestive Glands) :

• ଖାଦ୍ୟକୁ ସରଳୀକୃତ କରିବା ପାଇଁ ପାକନଳୀ ମଧ୍ଯରେ ଅନେକଗୁଡ଼ିଏ ପାକଗ୍ରନ୍ଥି ଅଛି । ଯଥା –

(i) (Salivary Glands) :

• ମନୁଷ୍ୟର 3 ଯୋଡ଼ା ଲାଳଗ୍ରନ୍ଥି ରହିଛି ଏବଂ ଏହାର ବାହିକା (ducts)ଗୁଡ଼ିକ ମୁଖଗହ୍ଵର ମଧ୍ୟକୁ ଖୋଲି ରହିଥାଏ ।
• ଏହି ଗ୍ରନ୍ଥିରୁ କ୍ଷରିତ ଲାଳ ଖାଦ୍ୟକୁ ପିଚ୍ଛିଳ ଓ ମଣ୍ଡପରି କରିଦିଏ ।
• ଲାଳରେ ଥିବା ପାଚକ ଏନ୍‌ଜାଇମ୍‌କୁ ଟାୟାଲିନ୍ (Ptyalin) ବା ସାଲାଇଭାରି ଆମାଇଲେଜ୍ କୁହାଯାଏ ।

(ii) ଜଠର ଗ୍ରନ୍ଥି (Gastric Glands) :

• ଏହି ଗ୍ରନ୍ଥିରୁ କ୍ଷରିତ ହେଉଥ‌ିବା ରସକୁ ପାଚକ ରସ କୁହାଯାଏ । ଏଥିରେ ଲବଣାମ୍ଳ (HCl) ସହିତ ପେପସିନ୍ ଓ ଲାଇପେଜ୍ ଏନ୍‌ଜାଇମ୍ ରହିଛି ।
• ଏଗୁଡ଼ିକ ପାଚକ ରସ (Gastric juice) ଓ ଲବଣାମ୍ଳ (HCI) କ୍ଷରଣ କରିଥା’ନ୍ତି ।

(iii) (Liver) :

• ଏହା ଶରୀରର ବୃହତ୍ତମ ଗ୍ରନ୍ଥି ଏବଂ ଏହା ଉଦର ଗହ୍ଵରର ଉପରିଭାଗର ଡାହାଣପାର୍ଶ୍ଵରେ ଅବସ୍ଥିତ । ଏହାର ବର୍ଣ୍ଣ ଲୋହିତ ବାଦାମୀ ।
• ଏହା ପିତ୍ତ ରସ କ୍ଷରଣ କରେ ।

(iv) ଅଗ୍ନ୍ୟାଶୟ (Pancreas) :

• ଏହା ଏକ ମିଶ୍ରିତ ଗ୍ରନ୍ଥି ।
• ଏହା ମଧ୍ଯ ଖାଦ୍ୟନଳୀ ବାହାରେ ରହିଛି । ଏଥୁରୁ ଉଭୟ ଏନ୍‌ଜାଇମ୍ ଓ ହରମୋନ୍ କ୍ଷରିତ ହୁଏ । ଅଗ୍ନ୍ୟାଶୟ ରସରେ ଆମାଇଲେଜ, ଲାଇପେଜ୍ ଏବଂ ପ୍ରୋଟିଏଜ୍ ପରି ଖାଦ୍ୟ ହଜମକାରୀ ଏନ୍‌ଜାଇମ୍ ରହିଛନ୍ତି ।

→ ଆନ୍ତ୍ରିକ ଗ୍ରନ୍ଥି (Intestinal gland) :

• କ୍ଷୁଦ୍ରାନ୍ତ୍ରରେ ଥ‌ିବା ଆନ୍ତ୍ରିକ ଗ୍ରନ୍ଥିଗୁଡ଼ିକରୁ ଆର୍ଥିକ ରସ କ୍ଷରିତ ହୁଏ । ଏହି ରସରେ ଥ‌ିବା ବିଭିନ୍ନ ପ୍ରକାରର ଏନ୍‌ଜାଇମ୍ ହଜମକ୍ରିୟା ଶେଷ କରନ୍ତି ।

→ ପାଚନ କ୍ରିୟା (Digestion) :

• ଆମେ ଖାଉଥ‌ିବା ଖାଦ୍ୟରେ ଶ୍ଵେତସାର, ସ୍ନେହସାର, ପୁଷ୍ଟିସାର, ଭିଟାମିନ୍, ଧାତବ ଲବଣ ଓ ଜଳ ରହିଥାଏ । ଖାଦ୍ୟ ହଜମର ବିଭିନ୍ନ ପ୍ରକ୍ରିୟାଗୁନିକ
• ହେଲା : ଖାଦ୍ୟ ଗ୍ରହଣ, ପାକକ୍ରିୟା, ଅବଶୋଷଣ, ଆତ୍ମୀକରଣ ଓ ମଳତ୍ୟାଗ ।

(A) ମୁଖଗହ୍ଵର (Buccal Cavity) :

• ଏଠାରେ ଖାଦ୍ୟ ଚର୍ବିତ ଓ ପେଷିତ ହେବା ସଙ୍ଗେ ସଙ୍ଗେ ଟାୟାଲିନ୍‌ର କାର୍ଯ୍ୟକାରିତା ହାର ବୃଦ୍ଧି କରେ ।
• ଖାଦ୍ୟରେ ଲାଳ ମିଶିବାଦ୍ୱାରା ଟାୟାଲିନ୍ ପ୍ରାୟ 30-40 ଭାଗ ମଣ୍ଡଦ (Starch)କୁ ମାଲ୍‌ଟୋଜ୍ (Maltose)ରେ ପରିଣତ କରେ ।

(B) (Stomach) :
ଭାଙ୍ଗି ଅତି ସୂକ୍ଷ୍ମଖଣ୍ଡରେ ପରିଣତ ହୁଏ । ପାକସ୍ଥଳୀରୁ ନିସୃତ ପାଚକ ରସ ଖାଦ୍ୟ ସହିତ ମିଶି ଏହାକୁ ଏକ ପ୍ରକାର ତରଳ ମଣ୍ଡ ବା ଚାଇମରେ ପରିଣତ କରେ । ଲବଣାମ୍ଳ (HCl) ପାକମଣ୍ଡକୁ ଅମ୍ଳାତ୍ମକ କରିବା ସହିତ ଜୀବାଣୁ ନାଶ କରେ । ପାଚକରସରେ ଦୁଇ ପ୍ରକାର ଏନ୍‌ଜାଇମ୍ ଥାଏ – ପେପ୍‌ସିନ୍ ଓ ଲାଇପେଜ୍ । ପେପ୍‌ସିନ୍ ଲବଣାମ୍ଳ ମାଧ୍ୟମରେ ସକ୍ରିୟ ହୁଏ ଓ ପ୍ରୋଟିନ୍ ଖାଦ୍ୟକୁ ପ୍ରୋଟିଓଜେସ୍ ଓ ପେପ୍‌ନ୍‌ରେ ପରିଣତ କରେ ।

(C) ଗ୍ରହଣୀ :
କ୍ଷୁଦ୍ରାନ୍ତର ଗ୍ରହଣୀଠାରେ ଯକୃତରୁ କ୍ଷରିତ ପିତ୍ତ ଓ ଅଗ୍ନ୍ୟାଶୟରୁ କ୍ଷରିତ ଅଗ୍ନ୍ୟାଶୟ ରସ ଖାଦ୍ୟରେ ଆସି ମିଶେ । ପିତ୍ତରେ ଥ‌ିବା ପିତ୍ତ ଲବଣ ଖାଦ୍ୟର ଅମ୍ଳତ୍ଵ ଦୂର କରେ ଓ ସ୍ନେହସାର ଜାତୀୟ ଖାଦ୍ୟର ଅବଦ୍ରବୀକରଣ ବା ଇମଲ୍ଟିଫିକେସନ୍ (Emulsification) କରାଇଥାଏ ।

(D) ଜେଜୁନମ୍ ଓ ଇଲିୟମ୍ :
ଏହି ସ୍ଥାନରେ ସମସ୍ତ ଖାଦ୍ୟର ହଜମ ପ୍ରକ୍ରିୟା ସମ୍ପୂର୍ଣ୍ଣ ହୋଇଥାଏ । ଜେଜୁନମ୍ ଓ ଇଲିୟମ୍‌ରୁ କ୍ଷରିତ ଆର୍ଥିକ ରସରେ ରହିଥ‌ିବା ବିଭିନ୍ନ ପ୍ରକାର ଏନଜାଇମ୍ ହଜମ ହୋଇନଥୁବା ଅବଶିଷ୍ଟ ଖାଦ୍ୟକୁ ସମ୍ପୂର୍ଣ ହଜମ କରିଥା’ନ୍ତି । ଏଠାରେ ହେଉଥ‌ିବା ହଜମ ପ୍ରକ୍ରିୟାଟି :

(E) ବୃହଦନ୍ତ୍ର :
ଖାଦ୍ୟ ବୃହଦନ୍ତ୍ରଠାରେ ପହଞ୍ଚିଲା ବେଳକୁ ଏହା ହଜମ ହୋଇ ସରଳୀକୃତ ଖାଦ୍ୟରେ ପରିଣତ ହୋଇଥାଏ ।

(v) (Absorption) :
ସମସ୍ତ ସରଳୀକୃତ ଖାଦ୍ୟ, ଭିଟାମିନ୍, ଧାତବ ଲବଣ ଓ ଜଳ ଇତ୍ୟାଦି ଆହାରନଳୀର କାନ୍ଥ ବାଟ ଦେଇ ରକ୍ତ ମଧ୍ୟକୁ ପ୍ରବେଶ କରିବା ପ୍ରକ୍ରିୟାକୁ ଅବଶୋଷଣ କୁହାଯାଏ । ଏହି ପ୍ରକ୍ରିୟା ନିଷ୍କ୍ରିୟ ଅବଶୋଷଣ ଓ ସକ୍ରିୟ ଅବଶୋଷଣଦ୍ୱାରା ହୋଇଥାଏ ।

(vi) (Assimilation) :

• ଅବଶୋଷଣ ପରେ ସରଳୀକୃତ ଖାଦ୍ୟ ରକ୍ତଦ୍ୱାରା ବାହିତ ହୋଇ ଯକୃତରେ ପହଞ୍ଚେ । ଯକୃତରୁ ଏହା ଶରୀରର ବିଭିନ୍ନ ଅଂଶରେ ପହଞ୍ଚିଥାଏ ଏବଂ ଶକ୍ତିମୋଚନ ଓ ଅନ୍ୟ କାର୍ଯ୍ୟରେ ନିୟୋଜିତ ହୋଇଥାଏ । ଖାଦ୍ୟର ଏହି ବିନିଯୋଗ
• ଅଧିକାଂଶ ଏମିନୋ ଅମ୍ଳ ପୁଷ୍ଟିସାର ସଂଶ୍ଳେଷଣରେ ବ୍ୟବହୃତ ହୁଏ ଯାହାକି ଶରୀର ବୃଦ୍ଧି ଓ ଟିସୁର ପୁନଃନିର୍ମାଣରେ ସହାୟକ ହୁଏ । ବଳକା ଏମିନୋ ଅମ୍ଳ ଯକୃତରେ ୟୁରିଆରେ ପରିଣତ ହୁଏ ।

(vii) (Egestion) :
ଏକକାଳୀନ ନିମ୍ନଲିଖ୍ ଘଟଣାବଳୀଦ୍ଵାରା ମଳ ନିଷ୍କାସନ ହୋଇଥାଏ ।

• ମଳଦ୍ଵାର ଚାରିପଟେ ରହିଥ‌ିବା ସଂକୋଚନ ପେଶୀର ଶିଥୁଳନ,
• ମଳାଶୟ ପେଶୀର ସଂକୋଚନ,
• ଉଦରପେଶୀ ଓ ମଧ୍ଯଚ୍ଛଦାର ସଂକୋଚନ ସହିତ ସାମୟିକ ଶ୍ଵାସ ବିରାମ ।

ମାଂସ ହଜମ କରୁଥିବା ଏନଜାଇମ୍ ଆମ ପାକସ୍ଥଳୀକୁ ହଜମ କରିପାରେ ନାହିଁ କାରଣ :

• ପୁଷ୍ଟିସାର ହଜମ କରୁଥିବା ପ୍ରୋଟିଏଜ୍ ଜାତୀୟ ଏନଜାଇମ୍ ନିଷ୍କ୍ରିୟ ଅବସ୍ଥାରେ କ୍ଷରିତ ହୋଇଥାଏ । ପାକସ୍ଥଳୀର ଅମ୍ଳୀୟ ପରିବେଶରେ ଏହା ସକ୍ରିୟ ହୁଏ ଓ ପାକସ୍ଥଳୀରେ ଖାଦ୍ୟ ପହଞ୍ଚିଲେ ସାଧାରଣତଃ ଏନ୍‌ଜାଇମ୍ କ୍ଷରଣ
• ଆମ ପାକସ୍ଥଳୀରେ ଅନେକ ଶ୍ଳେଷ୍ମକ ବା ମ୍ୟୁକସ୍ ଗ୍ରନ୍ଥି ରହିଛି । ସେଥୁରୁ କ୍ଷରିତ ମ୍ୟୁକସ୍ ଅମ୍ଳୀୟ ପରିବେଶ ତଥା ଏନ୍‌ଜାଇମ୍ ପ୍ରଭାବରୁ ପାକସ୍ଥଳୀକୁ ରକ୍ଷାକରେ ।
• ପାକସ୍ଥଳୀର କୋଷମାନଙ୍କ ମଧ୍ୟରେ ଥ‌ିବା ନିବିଡ଼ ବନ୍ଧନ ଯୋଗୁଁ ସହଜରେ ପେପ୍‌ସିନ୍ ପାକସ୍ଥଳୀ କାନ୍ଥ ଭିତରକୁ ଟିସୁ କ୍ଷୟ କରିପାରେ ନାହିଁ ।
• ଏଥ୍ ସହିତ ପାକସ୍ଥଳୀର କୋଷ ପ୍ରତି ଦୁଇ ବା ତିନିଦିନ ବ୍ୟବଧାନରେ ନୂଆ କୋଷଦ୍ଵାରା ପୁନଃସ୍ଥାପିତ ହୁଅନ୍ତି । ଏଥ୍ ଯୋଗୁଁ ଆମ ପାକସ୍ଥଳୀ ପେପ୍‌ସିନ୍ ଏନ୍‌ଜାଇମ୍ଵାରା ହଜମ ହୁଏନାହିଁ ।

Odisha State Board CHSE Odisha Class 11 Political Science Solutions Unit 3 Indian Constitution Short Answer Questions.

CHSE Odisha 11th Class Political Science Unit 3 Understanding Political Theory Short Answer Questions

Short Question With Answers

Question 1.
What were the functions of the constituent assembly of India?
Answer:
The constitution assembly was formed to prepare the new constitution of India and To act as the union legislature till the new parliament was formed.

Question 2.
What was the importance of the Drafting committee?
Answer:
The drafting committee played an important role in drafting the new constitution of India. It was the future ruling pattern of India.

Question 3.
What do you mean by objective resolution?
Answer:
Objective resolution refers to the aims and objectives of the constitutional frames expressed in the form of a resolution. It was approved by the constituent assembly on 22nd January 1947.

Question 4.
Why Indian constitution has been so large?
Answer:
The constitution of India is so large because it contains provisions both for the union government and states. The length of the constitution increased in view of the detailed analysis of every provision to make it clear to the people.

Question 5.
What is an ideal constitution?
Answer:
An ideal constitution is a document that has the ability to develop and V change in accordance with changes in time and circumstances. Its language must be simple clear andunamigous

Question 6.
What is the preamble?
Answer:
A preamble is a brief introduction about the constitution. It contains ideals and objectives of the constitution in a nutshell.

Question 7.
What does the term we the people of India imply?
Answer:
The term we the people of India implies the source of the constitution and its democratic character. It was framed by a group of representatives of Indian people.

Question 8.
What are the main sources of the constitution?
Answer:
The Government of India Act. 1935. The parliamentary statutes and debates. The constitution of UK, Canada, Australia, Ireland, Germany, Spain and South Africa etc.

Question 9.
Why India is called a secular state?
Answer:
India is called a secular state because
There is no state religion in India and All religious communities are treated equally by the state. People enjoy the freedom of religion and worship.

Question 10
Why India is called a sovereign state?
Answer:
India is called a sovereign state because it is independent and free from the influence of any foreign country. The decision of the government of India is found delating internal administration and foreign policy.

Question 11.
Why India is called a socialist state?
Answer:
India is called a socialistic state because, it seeks to provide social, economic, and political justice to the people. The government gives priority to the public sector and seeks to abolish economic exploitation and provide basic minimum needs to all.

Question 12.
Why India is called a democracy?
Answer:
India is called a democracy because the constitution has set up parliamentary representative democracy in India. The people enjoy fundamental rights and the media and judiciary remain free from Govt, control.

Question 13.
Why India is called a Republic?
Answer:
India is called a republic because the head of state, the president is elected by the people indirectly Again any ordinary citizen can contest and assume the office of the president of India.

Question 14.
Why Indian constitution is called an enacted constitution?
Answer:
Indian constitution is called an enacted constitution because it was ‘ framed by a constituent assembly.’ It was enacted on 26th November 1949 by the constituent assembly.

Question 15.
India is a union of states?
Answer:
Art. 1 declares India as a union of states. That means the federal structure of ” India can’t be changed by the decision of states.

Question 16.
Why India is called a quasi-federal state?
Answer:
Prof. K.C. where describes India as a quasi-federal state. It means that India is organized on federal lines but it works as a unitary state.

Question 17.
Is the Indian constitution rigid?
Answer:
Indian constitution can’t be considered exclusively either as a rigid or flexible constitution. The procedure of amendment is a mixture of both rigidity and flexibility.

Question 18.
What is single citizenship?
Answer:
Single citizenship means only the union government has the power to grant citizenship. It is found in a unitary state, but in India single citizenship is preferred to maintain national unity and integrity.

Question 19.
What is judicial review?
Answer:
Judicial review refers to the power of the supreme court to examine the constitutional validity of the law. If it finds any law or decision violating the constitution the court declares such law unconstitutional.

Question 20.
What do you mean by fundamental rights?
Answer:
The fundamental rights are the most valuable rights which are mentioned in part – III of the constitution. These rights are justiciable in nature, therefore in case of violation, the court takes immediate redressal measures.

Question 21.
What is Right to Equality?
Answer:
The right to equality is a fundamental right which is guaranteed under Art 14 to 18 of the constitution. This right is available both for citizens.

Question 22.
What is equality before law?
Answer:
Equality before law means all are equal in the eyes of law. The law courts the judges and the legal system gives equal protection to all citizens.

Question 23.
Importance of Art. 19?
Answer:
Art. 19 guarantees six fundamental freedoms to Indian citizens. These include freedom of speech and expression freedom to assemble peacefully without arms, freedom of association, freedom of movement, freedom of settlement & freedom of profession trade or business.

Question 24.
Traffic in human beings?
Answer:
Traffic in human beings means exploitation and unlawful treatment of weaker sections of society. It prohibits men and upper classes from exploiting women, children, and backward classes.

Question 25.
How the fundamental rights differ from legal rights?
Answer:
The fundamental rights are guaranteed and protected by the institution, but the legal rights are protected by law. The legal rights can be amended by ordinary legislation, but fundamental rights can be amended only by constitutional amendment.

Question 26.
Which fundamental rights are available both for citizens and aliens?
Answer:
Right to equality under Art. 14 and Right to life liberty and property under Art. 21 are available both for citizens and aliens

Question 27.
Right to education?
Answer:
Right to education is now a fundamental right under Art. 21 (A) It is inserted into the fundamental rights by the 86th amendment act. 2002. It provides for free and compulsory education to all children below 14 years of age.

Question 28.
Right against exploitation?
Answer:
This right is guaranteed under Art. 23 and 24 of the constitution. It seeks to give protection to the weaker sections of society, including women, children and backward classes from the exploitation of rich and male-dominated society.

Question 29.
What is protective discrimination?
Answer:
The constitution of India under Art. 15 (3) and provide for protective discrimination. It enables the scheduled castes, scheduled tribes, women- and backward classes to avail special reservations in admission to educational institutions and in public service.

Question 30.
Habeas Corpus?
Answer:
Habeas Corpus is a writ issued by a superior court against any public authority. It is issued against unlawful arrest and detention.

Question 31.
Mandamus?
Answer:
The writ of Mandamus is issued by a superior court to any person or ‘ public authority to perform a legal duty. It is a direction to perform ministerial acts.

Question 32.
What is Prohibition?
Answer:
The writ of prohibition is issued either by Supreme Court or High Court to an inferior court against excessive jurisdiction. It prevents a lower court from handling cases beyond the jurisdiction

Question 33.
Certiorari?
Answer:
A certiorari is a writ issued by the superior court to any lower court against excessive jurisdiction. It is issued to quash the order and decision of the court or tribunal.

Question 34.
Quo-Warranto?
Answer:
The writ of quo warm to is issued by a superior court to any public authority against the illegal assumption of public office. It prohibits illegal appointments to public service.

Question 35.
Importance of Art. 32?
Answer:
The Indian Constitution Under Art. 32 grants right to constitutional remedies. As per the article, in the case of. violation of the fundamental rights of a citizen, he can move to the Supreme Court for immediate redressal.

Question 36.
Objectives of Directive Principles?
Answer:
The objectives of directive principles of state policy are To make India a welfare state and To create conditions for socio-economic democracy in India.

Question 37.
Fundamental-Duties?
Answer:
The fundamental duties are the moral responsibilities of the citizens towards the state. These are non-justiciable in nature.

Question 38.
Right to the property?
Answer:
The right to property was a fundamental right up to 1978, but it was deleted in 1978 by 44th Amendment Act. Now it is a legal duty under Art. 300 A.

Question 39.
Right to Education?
Answer:
Right to Education is a fundamental right under Art. 21 (A). It provides for free and compulsory education to all children belonging to the age group of 6 to 14 years.

Question 40.
Right to life?
Answer:
Right to life is a fundamental right under Art. 21. It states that no one shall be deprived of his life and liberty except, according to procedure established by law.

Question 41.
Right to Information Act. 2005?
Answer:
The Right to Information Act, 2005 seeks to promote transparency and accountability in the working of the government. It helps in containing corruption and makes the citizens aware about the activities of the government.

Question 42.
What is preventive detention?
Answer:
The constitution of India under Art 22 provides for preventive detention of criminal and anti-socials beyond 24 hours. Under this provision any person whose presence is apprehensive of creating social disorder and violence, he may be kept under legal custody for three months even without violating law.

Question 43.
What constitutes the basic structure of the constitution?
Answer:
Basic structure comprises of some values ideals and principles of the constitution which lay its foundation, According to eminent justice, it includes parliamentary democracy, fundamental rights, preamble, secularism, republican model, independent judiciary and centralized federation, etc.

Question 44.
What is free legal aid?
Answer:
The constitution of India under Art. 39A under the Directive Principle makes provision for free legal aid to the poor and underprivileged sections of society; Under the provision, the state government bears the cost of fighting legal battles against those exploiting women, poor and distressed people.

Question 45.
Constituent Assembly of India?
Answer:
The new constitution of India was framed by die constituent Assembly, (b) It comprises of all the eminent lawyers. Intellectuals, social activists, and political leaders of India of that time. It was a representative body that prepared the constitution within 2 years 11 months and 18 days. It played the role of parliament till the new parliament was elected. Its members were elected indirectly by the provincial legislatures on the basis of population.

Question 46.
Cabinet mission plan?
Answer:
Cabinet mission. came to India in the year 1946 to discuss about the grant of independence to India. Prime minister clement allee sent three of his cabinet minister, Sir Stafford Cripps, A’.V. Alexander and Lord Pathik Lawrence as members of the mission. The mission held discussions with Indian leaders, leaders of the Muslim League, and administrators about the ways and means to concede independence. The mission proposed for a ‘Constituent assembly to be formed to prepare the new constitution of India. It recommended for a federal setup in India with Indian provinces and princely states.

Question 47.
Drafting committee?
Answer:
The drafting committee was instrumental for framing the new. constitution of India. It comprises of Dr. B .R.Ambedkar as the chairman and N. Gopalswamy Ayengarm, Alladi Krishnaswamy, Nyer, K.M. Munsi, Mahammad Saddik, N. Madhab Rao and T.T. Krishiiamachari as members. This committee prepared the draft of the whole constitution and got it approved. It had 55 sessions continuing for 114 days and on 4th November 1948 submitted the draft constitution for approved. Dr. Ambedkar played a leading role as its chairman for which he is regarded as the father of Indian constitution.

Question 48.
Objective Resolution?
Answer:
Objective Resolution of the constituent Assembly was initiated by Pandit Nehru on 13th December 1946. It was approved on. 22nd January 1947 by the constituent assembly. This resolution contained the aims and aspirations of the founding fathers relating to the future of India. It proposed to make India, a sovereign Independent Republic. Besides, it also resolved to ensure social political and economic justice to the people of India along with liberty and equality.

Question 49.
Write at least five important features of Indian Constitution?
Answer:

• Longest written constitution.
• A balance between rigidity and flexibility
• Federal in form but unitary in spirit
• Parliamentary democracy; and
• Secular State

Question 50.
What does the preamble to the constitution imply?
Answer:
The preamble implies an introduction to the Constitution. It embodies the objective, ideals, sentiments and aspirations of the nation. It is a key to understanding the nature and spirit of the Indian Policy. It speaks about the source of the Constitution and the date of its adoption. The preamble indicates the general purpose for which people have ordained and established Constitution.

Question 51.
What are the source of the Indian Constitution?
Answer:
The contents of the Indian Constitution have been derived from different sources out of which the important ones are given below.
The Government of India Act, of 1935 has been the most important source of the Constitution. The British Constitution has influenced it the most. The fundamental rights have come from the American constitution. The Irish constitution, the Weimar Constitution of Germany the Canadian Constitution and the Constitution of the South African Republic have also influenced the Indian Constitution.

Question 52.
How does the Preamble depict the characteristics of Indian Constitution?
Answer:
The preamble outlines the following characteristics of Indian Constitution. India is a sovereign independent community. India is a republic. India has a democratic form of government. The constitution ensures justice, liberty, equality and fraternity. It seeks to harmonize dignity of the individual with unity of the nation. It establishes popular sovereignty and seeks to follow socialistic and secular principles.

Question 53.
India is a Sovereign Socialist Secular Democratic Republic Discuss?
Answer:
The Preamble reads India as a Sovereign, Socialist Secular Democratic Republic. India is sovereign both internally and externally and it believes in socialistic principles. India has no state religion and the Constitution grants equal status to all religions. Indian policy is organized on democratic principles and the President being the head of state is elected hence it is a republic.

Question 54.
Why is Indian Constitution so long?
Answer:
Indian constitution is the longest written Constitution in the world having 395 Articles and 12 Schedules. The factors responsible for the extra length of the Constitution are as follows. The constitution is meant both for the Union and the States. Everything in the Constitution has been discussed in detail.

The diversity of the Indian culture necessitated special provisions for which the Constitution has been so long. Besides the above factors, detailed chapters on fundamental rights, Directive Principles, emergency provisions, center-state relations and fundamental duties have added to the size of the constitution.

Question 55.
Why is Indian Constitution supposed to be a bag of borrowings?
Answer:
The Indian Constitution was framed following the major democratic constitution of the world. The British Constitution America, Irish, Australian and Canadian Constitutions, etc. have significantly influenced the framers, but that does not mean that the principles and ideals of the Constitution are borrowed: The framers have borrowed most of the provisions from Western countries and modified them to suit to Indian conditions and the people. It will be wrong to brand as a borrowed constitution.

Question 56.
Indian Constitution is federal in form but unitary in spirit. Discuss?
Answer:
Indian constitution has designed the country on the principles of a federation but it works more or less as a unitary state. The framers adopted a federal form of government on account of its vastness but declared it as a union of states. Despite all federal features, the union government is given an upper hand in every sphere. The union Govt enjoys more powers and it can at times change the federal structure into a unitary one. The framers have made a happy blend between unitarism and federalism for which it is supposed to be federal in form but unitary in spirit.

Question 57.
Why is India called a Quasi Federal State?
Answer:
A quasi-federal state is one which is neither completely unitary nor federal in character. Prof. K.C. where has criticized India’s federal character as was quasi-federal. India is organized on the basis of the federation but works on unitary lines. The union government enjoys more powers than the states and the framer can suspend the state government on various grounds. The Union Govt, through the office of the Governor, All India Services, Planning Commission, National Development Council and Finance Commission, etc. can influence the Govt, at the state. Therefore, India is called a quasi-federal state.

Question 58.
Is Indian Constitution a rigid one?
Answer:
No, Indian Constitution does not come along the lines of a rigid Constitution as that of the U.S.A. Most parts of the Constitution can be amended by simple procedure of legislation. Only the federal features of the Constitution are rigid. Those matters can be amended if a majority of both houses of Parliament coupled with the 2/3rd majority of those present and voting support the motion.

Therefore, the Constitutional amendment is sent to the state legislatures for ratification. If at least half of the states approve the proposal the amendment is effected. This rigid procedure applies only to a few items.

Question 59.
Indian Constitution is flexible. Discuss?
Answer:
A flexible Constitution is one which can be amended easily, by the simple procedure of legislation. Most parts of the Constitution can be amended Iggy this process but there are still important matters which need to be amended by the rigid process. As the constitutional framers have made a compromise between rigidity and flexibility it can not be described as i flexible Constitution.

Question 60.
Briefly state the Preamble of the Indian Constitution?
Answer:
The Preamble of the Indian Constitution reads as follows: “WE ‘THE PEOPLE OF INDIA” laving solemnly resolved to constitute India intoa SOVEREIGN SOCIALIST SECULAR DEMOCRATIC REPUBLIC AND TO SECURE TO ALL ITS CITIZENS. JUSTICE, Social, Economic and Political LIBERTY of thought, expression, faith, belief and worship.

EQUALITY of status and opportunity, land to promote among them all FRATERNITY assuring the dignity of the individual and the unity and integrity of the nation. IN OUR CONSTITUENT ASSEMBLY, this twenty-sixth day of November 1949, do hereby ADOPT ENACT AND GIVE TO OURSELVES THIS CONSTITUTION.

Question 61.
What is the importance of the term ‘We the people of India’?
Answer:
The Preamble starts with the phrase ‘We the people of India which illustrates that the people of India are the maker of the Constitution. It speaks about the representative character of the Constitution and accepts people as the ultimate sovereign. The constitution is a popular document which is not imposed on the people but deliberately prepared by a representative Constituent Assembly.

Question 62.
Is India is a sovereign state?
Answer:
Yes, India is a sovereign state and the preamble of the constitution declares about its sovereign character. Internally and externally. India is supreme. Externally, the country is free from any outside authority and it has accepted the membership of international organizations voluntarily internally, it is competent to adopt its domestic policies and regulate the behavior of its nationals and organizations.

Question 63.
Is India is a Secular State?
Answer:
Yes, India is a secular state. A secular state is one which is neither anti-religious nor irreligious. It grants equal status and freedom to, all religions. There is no state religion in India and no religious discrimination is practiced. The Constitution has guaranteed right to freedom of religion to the citizens which symbolizes the secular character of the constitution.

Question 64.
Why is lndia called a democratic republic?
Answer:
The Preamble declares India as a democratic republic. The Indian political system is organized on a comprehensive democratic basis. The parliament and the state legislature are elective bodies and the franchise is extended to all adult citizens universally. The Govt, of India, is elected by the people periodically and remains. responsible.to them. It is a republic because the President being the head of State is elected indirectly. Thus India is called a democratic republic.

Question 65.
Is India a Welfare State?
Answer:
Yes, India is a secular state ordained under Art. 38 of the Constitution. The Directive Principles also embody the principles of a welfare state. The constitution states that the ownership and control of material resources shall be distributed equally to subserve common good. The Govt provides special assistance to the educationally, and economically backward sections of the community. The five-year plans and the socialistic principles are implemented in the country to make India a welfare state.

Question 66.
What is single citizenship?
Answer:
Single citizenship means that in India the power to grant citizenship has been conferred upon the union government only. The state has no authority in this regard. All citizens residing anywhere within India irrespective of their residence or place of birth, are the citizens of India. This idea is supposed to promote a sense of unity among Indians.

Question 67.
What are the five pillars of the Constitution?
Answer:
The five pillars of the constitution are

• the election commission,
• the Finance Commission
• the Union Public Service Commission
• the Attorney General and
• the Auditor-General of India.

These constitute the heart of the democratic structure.

Question 68.
What are the basic philosophy of the Constitution?
Answer:
The basic principles embodying the philosophy of the constitution are as follows:

• Popular sovereignty,
• Federal system
• Fundamental rights of the citizens,
• Directive principles of state policy,
• Judicial independence
• Parliamentary system
• Supremacy of the Union Government.

Question 69.
How the Indian Constitution can be amended?
Answer:
The Indian constitution can be amended by the Parliament under Art. 368. The parliament by required majority can make addition, variation or repeal any provision of the constitution. Such a proposal can be initiated in either House of Parliament and after approval, it is submitted to the President for assent. The President, can’t reject such a proposal and after President’s assent, necessary amendments may be effected.

Question 70.
Why India is called a socialist state?
Answer:
India is called a socialist state, because of the following reasons. The Govt, of India, acts on socialistic lines. The Govt is committed to securing socio-economic and political justice to the people by ending all forms of exploitation. It undertakes economic planning to ensure equitable distribution of wealth and income.

Question 71.
What is the importance of the Preamble to the constitution?
Answer:
A preamble is an introduction to the constitution. It underlines the philosophical foundations of the constitution and its objectives. It outlines in a nutshell the ideals and objectives of our constitution. It lays down the pattern of our political setup, that is to make India a sovereign, socialist, secular, democratic republic. It speaks about the source of constitution And the date of its, adoption.

Question 72.
Is, the Preamble a part of the constitution?
Answer:
This is a controversial question. As per the decision of the Supreme Court on the transfer of the Berubari Union and exchange of Enclaves, the Preamble is not a part of the constitution. But the apex court modified its decision: in the Keshavananda Bharati case and regarded the preamble as a part of the constitution. In fact, it forms a part of the basic structure as it defines the. structure and philosophy of the constitution.

Question 73.
How the Constitution of India has safeguarded the interests of S.Cs and STs?
Answer:
The Indian constitution under Part XVI has specified special provisions for safeguarding the interests of Scheduled Castes Under Art – 330 seats have been reserved for them in the Lok Sabha and under Art. 331 and 332 in the State Legislatures. They are given special facilities to join public service, to get promotions, and to get admission into colleges, universities, and- professional institutions.

Question 74.
Which four new languages have been added to the VIIIth Schedule by the 100th Amendment Act?
Answer:
The four languages which have got an entry into the VIIIth Schedule by the 100th Amendment Act are, Bodo, Dogri, Maithili and Santhali.

Question 75.
Name five major sources of Indian Constitution?
Answer:
The five major sources of Indian Constitution are:

• The Govt, of India Act, 1935
• Provisions of foreign constitutions.
• Records of debates and discussions in the constituent Assembly.
• Parliamentary statutes and judicial decisions.
• The ideals and values of freedom struggle.

Question 76.
86th Constitutional Amendment, 2002?
Answer:
The Parliament passed the 86th Amendment Act, in 2002. It provides for Inclusion of Art. 21 (A) Whereby all children under the age group of 6 to 14 years of age are given the fundamental right of free and compulsory education. It added a new duty in Art. 51(A) increasing the number to 11. By this amendment, it has become the duty of the parents to send their children from 6 to 14 years of age to school.

Question 77.
What do you mean by fundamental Rights?
Answer:

• Fundamental Rights are those rights guaranteed in the constitution.
• It ensures the development of individual personality.
• These rights are guaranteed and protected by the state.
• The fundamental rights are superior to ordinary laws.
• These rights are the bedrock of Indian democracy.
• The Government cannot make laws violating any of these rights.

Question 78.
Name the six Fundamental Rights?
Answer:

• Right to Equality
• Right to Freedom
• Right against Exploitation
• Right of Freedom of Religion
• Educational and Cultural Rights
• Right to Constitutional Remedies

Question 79.
What do you mean by Right to equality?
Answer:
Right to equality is the first fundamental right guaranteed to the citizens. It refers to equality before law and equal protection of laws. If eliminates the possibility of all discrimination against a citizen on grounds of religion, race, sex, caste or place of birth. It guarantees equality of opportunity to all in matters of public employment. It seeks to abolish untouchability to ensure social equality. The constitution prohibits all titles and honors for the Indian except that of military or academic character to maintain proper equality.

Question 80.
What are the six freedom guaranteed under Art19?
Answer:
The six freedoms guaranteed under Art. 19 are:

• Freedom of speech and expression.
• Freedom to assemble peacefully without arms.
• Freedom to form associations or unions.
• Freedom to move freely throughout the territory of India.
• Freedom to reside and settle in any part of India.
• Freedom to practice any profession, occupation, trade, or business.

Question 81.
What does Right against Exploitation imply?
Answer
The right against exploitation is a fundamental right which seeks to prohibit all forms of exploitation of the children and women. It prohibits forced labor and traffic in human beings. It prevents child below 14 years to be employed in any factory or mine where there is danger to life. It also opposes the illegal use of women for immoral purposes. This right is meant for the weaker sections of the community.

Question 82.
What does the Right to Freedom of Religion imply?
Answer:
The Right to Freedom of Religion implies secular character of the state. It has been explained under four articles:

• Art. 25 states that all persons are equally entitled to freedom of conscience and the right to profess, propagate or practice any religion.
• Art. 26 grants the freedom to establish and maintain religious institutions for religious or charitable purposes.
• Art. 27 provides that, no person shall be ” compelled to pay any tax for the promotion of any particular religion.
• Art. 28 states that no religious instruction shall be provided in any educational institution wholly maintained by the state funds.

Question 83.
What is the meaning of Right to constitutional remedies?
Answer:
This is the sixth fundamental right which provides remedial measures for the enforcement of fundamental rights. This right is conferred under Art. 32 of the Constitution and it empowers the Supreme Court to uphold the fundamental rights of the citizens. If the fundamental rights of a citizen are violated he can move to the Supreme Court under Art. 32 or High Court under Art. 226 for redressal. The court can issue appropriate writs to provide- relief to the affected persons.

Question 84.
What are the different kinds of writs issued by the courts for the redressal of fundamental rights?
Answer:
There are five kinds of writs issued by the courts for the redressal of fundamental rights. These writs are

• Habeas Corpus
• Mandamus
• Prohibition
• Certiorari, and
• Quo-Warranto

Question 85.
What is the purpose of the writ of Habeas Corpus?
Answer:
The writ of Habeas Corpus is issued to maintain and enforce the fundamental rights of citizens. It is a Latin word which means to have one’s own body. The purpose of Habeas Corpus is to protect a citizen from unlawful arrest and detention. If a person is arrested or detained without any valid reason the court orders for his release by issuing this writ. It preserves the liberty of a person who is confined without legal justification.

Question 86.
What for the writ of Mandamus is issued?
Answer:
The writ of mandamus is issued by the court commanding a person or authority to do his duty. This writ is used for public purposes to enforce the performance of public duties. It also enforces some privacy rights when they are withheld by the public.

Question 87.
What is prohibition?
Answer:
It is a judicial writ issued by a superior court to an inferior court to prevent the lower court from usurping jurisdiction. The writ of prohibition is meant to check the possibility of abuse in a jurisdiction. If any case pending before the court is beyond its jurisdiction, the higher court by iásue of the writ prohibits the lower cÓurt not to hear such case.

Question 88.
What is Certiorari?
Answer:
A certiorari is a writ issued by a higher court to a lower count for the withdrawal of a case from the latter to the former. Such a writ may be issued even before the trial of the court comes to know that anything beyond the jurisdiction of the court is pending for decision before it. Both the writs of prohibition and certiorari are intended to deal with complaints of excess of jurisdiction.

Question 89.
What is the purpose of Quo warranto?
Answer:
Quo-warranto is a writ which is issued to prevent the illegal assumption of public office. Quo-warrantà’means by what authority. The court issuing the writ has to consider whether there has b&n usurpation of public office or not. It has been there even before the framing of the constitution.

Question 90.
Can the Parliament of India amend the fundamental rights?
Answer:
Yes, the Parliament of India can amend any portion of the fundamental rights excluding the basis structure of the Keshavananda Bharati and others Vs the State of Kerì1a held that the f parliament has right to an end all párts of the Constitution including Part Ill without destroying the basic structure of the constitution.

Question 91.
What do you mean by Directive Principles of State Policy?
Answer:
Directive Principles of State Policy is an important feature of the Indian constitution. These principles are discussed under part IV of the constitution and they are in the nature of constitutional directions o the state and central government to implement in administration. These directives are nonjustifiable but they are considered fundamental in the governance of the country These principles intend to play a positive role in the establishment of a socialist welfare state.

Question 92.
What Is the importance of Directive Principles?
Answer:
The Directive Principles of State Policy have immense utility and importance in making every modem state welfare state. These principles set the foundation of socio-economic democracy in India. These are not obligatory, but they are positive guidelines for the states to observe and implement them in the day-to-day administration of the state. They are not enforceable in any court but they are considered fundamental in the governance of the country.

Question 93.
Name of the socialistic principles of the Directives?
Answer:
The socialistic principles of the Directives contain the following.

• The ownership and control of the material resources of the community must be distributed to subserve common good.
• There must be equal pay for equal work for both men and women.
• The operation of the economic system should not lead to concentration of wealth and means of production to common detriment.
• The health and strength of the workers and tender age of children should not be abused.

Question 94.
Mention at least three Gandhian Principles of the Directives?
Answer:

• Organization of village Panchayats and to provide them with the power of self-government.
• Promotion of educational and economic interests of the S.C. and S.T.
• Promotion of cottage industry on individual and cooperative lines in the rural sector.

Question 95.
What constitutes the liberal principles of the directives?
Answer:
The liberal principles of the directive principles include:

• Separation of executive from the judiciary in public services.
• Provision for uniform civil code throughout the country.
• Protection of monuments and objects of historical and artistic importance.
• Promotion of international peace and security and maintaining adjustable and honorable relations with nations.
• To foster respect for international law and treaty obligations and settlement of international disputes through arbitration.

Question 96.
Fundamental Duties?
Answer:
The fundamental duties are mentioned in Part – IV A, under Art – 51 (A) of the constitution. These are inserted into the text of the constitution by the 42nd Amendment Act of 1976 on the recommendations of Dr. Swaran Singh’s Committee.These are moral in character. These duties are ten in number and in 2002, the 86th Amendment has inserted another duty to the list.

Question 97.
Features of Indian Fundamental Rights?
Answer:
The basic features of Indian fundamental rights can be discussed below:

• These rights are elaborate and comprehensive.
• Both negative and positive rights.
• These rights are not absolute.
• There are certain rights for minorities.
• They are binding upon the union, states, and other state authorities.

Question 98.
Right to Education?
Answer:
The Indian Constitution by the 86 Amendment Act of 2002 has added a new fundamental right under Art.- 21 A, called right to education. Under this article, the govt provides free and compulsory education to all children from the age group of 6 to 14 years in such as manner as the state may by law determine.

Question 99.
The Fundamental Rights in India are defective in many respects.
Answer:
The constitution under part – III has prescribed a comprehensive list of fundamental rights for Indian citizens. But there are certain weaknesses inherent in these rights as are given below:

• The constitution has imposed several limitations on fundamental rights.
• These rights are coded in difficult languages.
• There are no socioeconomic rights.
• The Parliament can amend fundamental rights.
• No mention about natural rights.

Odisha State Board CHSE Odisha Class 12 Sociology Solutions Unit 5 Change and Development in India Long Answer Questions.

CHSE Odisha 12th Class Sociology Unit 5 Change and Development in India Long Answer Questions

Long Questions With Answers

Question 1.
What is Globalisation ? Discuss the different impacts of globalisation on society?
Answer:
Globalisation is a vast, complex and multi- faceted term, hence it is difficult to give a comprehensive definition A prominent development is marked in the international marketing environment. Today is the trend towards increasing economic interdependence and globalisation of markets. Besides, as we know globalisation is not a new term. Though the term was not used there has always been a trend for business transcending national boundaries.

Globalisation refers to a trend towards international business which gives stresses international competition. It refers to the greatest use of markets and the forces of competition to coordinate economic activities. It also means opening up the economy to foreign competition. Globalisation means being able to manufacture in the most cost-effective way possible anywhere in the world.

At the same time, it also refers to being able to prepare raw materials and drawing management resources from the cheapest source anywhere in the world. It considered the entire world as its market. Hence, globalisation refers to a process of increasing economic integration and growing economic inter-dependence between countries in the world economy.

It is associated not only with increasing cross-border movements of goods and services, capital technology, information and people but also with an organisation of economic activities which cross national boundaries. Thus, globalisation is a kind of new world order and reduction of states or demise of the state system. In short, globalisation means thinking globally, producing and making globally.

Impact of Globalisation on Indian Society:
Before stepping to analyse the impact of globalisation on Indian society it will be pertinent to know when India, adopts the principle of globalisation. Under the pressure from International Monetary Fund and the World Bank and due to the increasing realisation of Indian planners, leaders and administrators that globalisation is a panacea for Indian poverty.

the Indian economy has been opening up to globalisation since the 1980s. Restricting the policy framework and industrial production, inflow of capital goods and technology, and growing foreign collaboration and foreign credit have to a great extent turned the economy of global developments. However, the following are the impacts of globalization.

Free market economy:
One of the immediate impacts of globalisation is that market became free and open to competition to all. There is an increasing realisation that a free market is better for the growth of the economy.

Encourages foreign investment:
Globalisation encourages foreign investment in different sectors of the Indian economy. Different sectors of the Indian economy are made open to different multinational or foreign companies. These companies enter India and invest a number of foreign capital because of which the Indian economy gets a boost.

More employment opportunities:
Because of globalisation a large number of foreign and multi-national companies have entered India and settled in different industries within India. This resulted in the creation of large-scale- employment in Indian society. Both direct and indirect employment is created.

Privatisation :
Globalisation also encourages privatisation in India. Because of globalisation disinvestment process set in. Privatisation refers to process whereby public operations are transferred to the private sector. Privatisation as a tool of public policy and as a concept has emerged only in recent times.

Liberalisation:
Another impact of globalisation is liberalisation. It aims to free the Indian industrial economy from the cobwebs of unnecessary bureaucratic control. It was introduced in Indian society to integrate the Indian economy with the world economy. It also aims at to remove restrictions on direct foreign investment as also to free domestic entrepreneurs from the restrictions of MRTP.

The decline of small and cottage industries:
Another impact of globalisation is the fall or decline of small and cottage industries. Being unable to face the competitions posed by the large scale and multinational companies the small and cottage industries wither away. They cannot insist on facing cutthroat competition from these industries.

Development of global culture:
Another important impact of globalisation is the development of a global culture. The whole world is a village in miniature.

The demise of the nation-state:
Globalisation resulted in the Denise of nation-states or states. It creates a new world order in which the state has little role to play. Thus, these are different impacts of globalisation.

Question 2.
Write a short note on urbanisation?
Answer:
Urbanisation refers to the process of growth in cities it terms of their social structure, population, physical outlay and cultural organisations. The physical and social structure of society to a large extent governs the nature of urbanisation. No doubt the nature of urbanism differs from security to society depending upon its cultural historicity and transition.

In the abstract, urbanisation is universally associated with a wide living that farmers privacy, anonymity with physic or unity to quickly adapt to new ideas or innovations and greater industrialism or sense of identity. It promotes plurality of the styles of a high degree of elitism in cultural life and dominates literally traditional learnings and skills in economic and cultural domains.

Socially it is not characterised by a predominance of conjugal families, or a faster pace of work pattern. Urbanism promotes the emergence of overlapping cultural and social enclaves based on principles of kinship, religion, language and religion etc. In which people interact different levels of social and cultural contexts.

The problem of studying neighbourhoods in cities and towns is a part of the tradition of urban community studies which is relatively new in India. While some socialists have studied small towns as communities, others have studied words or neighbourhoods in parts traditional cities revealing homogeneity in terms of casts and religious- groups. The community organisation in such neighbourhoods differed from that in neighbourhoods or in namely established housing estates.

A large percentage of the sector’s population felt that they are not bound by common interests and problems. This suggests that planned neighbourhoods need necessarily be communities. More intensive studies of both traditional neighbourhoods and new housing estates would be essential to understand the processes of continuity and change in traditional urbanism.

Question 3.
Explain globalization and discuss its merits and demerits?
Answer:
Some of the positive impacts, advantages or merits of the process of globalization are discussed below:
Improves efficiency:
Globalization brings efficiency in production and increases the efficiency of labourers. Free trade and the opening up of the economy are the main basis of globalization. This leads to specialization of production which is possible only due to the increase of efficiency of technology, labourers and management production of specialised products leads to export.

Eliminates poverty:
Globalization eliminates poverty and a higher growth rate. It gives a boost to the stagnant economy and eliminates poverty. Globalization creates more employment opportunities which means less poverty.

Promotes healthy competition:
Globalization creates or promotes healthy competition
among producers. Because it has given birth to the world market and a producer has to produce qualitative products or goods for the global market one could not produce qualitative products of the world-class standard has existence will be at stake, its motto is to compete perish. All this promotes healthy competition among producers.

Creates global village:
Globalization helps in the development of a global village. It increases interdependence among nation-states by breaking up national boundaries. It also aims at the establishment of one world and one government.

Improves financial situation:
Adequate finance is a precondition for development. A poor or developing country needs more finances to establish industrial ventures under globalization, and more financial help or assistance is available from different financial institutions like the IMF world bank. Bank Insurance and multinational corporations.

Multinational Corporations make direct investments and provide technical know-how, market management skill and many other associated benefits. All this helps to improve the financial situation of a developing country at the initial stage.

Encourages migration:
Globalization encourages cross-border migration of workers which makes up the deficiency of workers in developed countries. Knowledge, workers IT and computer engineers have a chance to move freely searching for good salary and better service conditions. migration reduces pressure on land and brought more foreign currencies to the country. At the same time, it also solves the problem of unemployment. This globalization by encouraging migration creates many benefits.

Strengthens democracy:
Globalization provides economic freedom to many. Because of better economic freedom more and more people actively, participate in the democratic process of the country. Thus, globalization has strengthened democracy.

Encourages international cooperation:
Encouraging cross-border migration and breaking up national boundaries and creating world market globalization increases international cooperation in different spheres which works towards world peace. Globalization has many benefits for its credit. But it is not an unmixed blessing.

Cities have criticised globalization due to its following disadvantages.
Increases inequality:
Globalization increases inequality both between rich and poor people as well as between developed and undeveloped nations. Under the process of globalization, the rich become richer and the poor become poorer. Similarly developed or rich countries enjoy all the benefits from the process of globalization and become richer or developed day by day whereas developing or poor countries suffer from misery and poverty They can’t compete with them in the market and become losers.

Closer of Industries:
Globalization encourages free trade which may lead to the closure of many domestic or small-scale industries. These industries fail to compete with the multinationals and become sick. Due to the process of globalization a large number of small-scale industries have been closed down. This leads to a decrease in production and creates unemployment.

Divides the world:
As a divisive process globalization divides the world into rich and poor nations or into underdeveloped, developing and developed nations. This division creates many problems and intensifies conflicts and tensions.

Creates uncertainties:
Globalization creates many uncertainties among workers industrialists among financial institutions. Workers fear retrenchment, industrialists fear the closure of their industries, and financial institutions fear a recession. All these uncertainties affect production and upset the economy of underdeveloped or developing countries.

Degenerates Human values:
Globalization degenerates human values, and progress or development is always viewed in terms of economic growth. Achievement of high economic growth is the only. Human values have little importance.

Exploitation:
It seems as if exploitation is the main objective of globalization. Under the process of globalization, multinational companies exploit poor workers as well as poor underdeveloped and developing nations. They take advantage of cheap labour and resources. Maternity of the poor lost their occupation.

Negative impacts on agriculture:
Globalization has several negative impacts on agriculture. Increasing emphasis on intensive irrigation more use of chemical fertilisers and pesticides abandoning traditional practices and increasing productivity have proved to be dangerous. Too much stress on the modernization of agriculture strongly affects agriculture as well as the environment.

Cultural erosion:
Globalisation led to the erosion of culture. Due to the impact of western culture, people become alien to their own culture. People become stronger in their own land.

Weakening of states:
Under the process of globalization power of state weakened state act as an agent of multinational companies.lt protects their interest and neglects the weaker sections. Multinational companies interfere with policies and their course.

Globalization created lot of economic insecurities like cutthroat competition, retrenchment, unemployment etc. Globalization led to an increase of crimes which threatens the existence of mankind. Control of the state on the domestic economy diminishes. Globalization causes Brain Drain which harms poor nations. Frequent and unnecessary interference multinational companies in the domestic affairs of developing countries acts as a threat to the unity and sovereignty of these countries.

Question 4.
What do you mean by liberalization? discuss its merits and demerits?
Answer:
Liberalization is another process of social change in India. lt is considered one of constituent parts of economic reforms. As an important economic concept liberalization is becoming more popular day by day. Liberalization is mainly a western economic theory. This process has entered India due to the process of modernization and western impact on Indian society.

However, the process of Liberalization began in India during the mid-seventies due to the crisis in the Indian economy. In order to save India from the acute financial crises the then prime minister Narsimha Rao and his finance minister Dr Manmohan Singh introduced liberalization in India, by accepting liberalization as the economic policy of the government of India.

As a result, liberalization became one of the aspects of the new economic policy gives stressing on reduction of governmental control on trade, business and industry. It abolished industrial licensing for all projects except a few like security strategic concerns. Liberalization refers to the reduction of governmental control to the minimum in matters of trade, business, investment and industry.

It aims at the abolition of licenses and permits raj and opening up of the national economy to the world economy. It means the government must shame private entrepreneurs while taking economic decisions.lt aims to set trade, business and industry free and to enable it to run on commercial lines.

The main idea behind the process of liberalization is that as trade and commerce are global subject hence it should not be confined to a particular boundary. Hence governmental restrictions over economic and commercial activities should be minimised to the maximum.

Merits of Liberalizations:

• Liberalization provides better opportunities for competition
• Liberalization helps to increase the export of the country.
• It helps in the free movement of goods and services.
• It has led to the production of Eqailitative products.
• It has led to rapid industrialization.
• It has provided maximum liberty to private enterprises.
• It helps to reduce unnecessary governmental control.

Demerits of Liberalization:

• Liberalization has negative impacts on small-scale industries.
• It has seriously damaged the power of the state.
• It has seriously affected our agriculture and environment.
• Under liberalization, the rich become richer and the poor become poorer which is not a good bend.
• It also creates unemployment and poverty.
• Conditions of unskilled labour is very pitiable under liberalization.

Thus, from the above, it is concluded that liberalization itself is neither good nor bad. It is a double-edged weapon. It can provide many benefits to mankind and can also be harmful and can spell disaster. Hence, much depends on its use and its own attitude towards it. But we should be conscious while following this economic principle.

Question 5.
Explain urbanization and discuss its causes and consequences?
Answer:
Urbanization is one of the most important processes of social change in India Because of the tremendous increase in urban population all over the world including India the importance of the process of urbanization has increased manifold. The term urbanization perhaps comes from the urban. The term urban is very ancient in nature.

Ordinarily, by urban area, we mean an area with a high-density of population. It also refers to a way of life. According to the 1981 census, an urban area refers to all places municipality corporation, cantoment board etc or an area which has a minimum population of5000 and at least 75 per cent of the male working population is engaged in non-agricultural activities and a density of population at least 400 persons per sq. KM. Urban centuries or cities are very ancient in nature.

There were cities of urban centres in ancient civilization. 5000 years ago there was a city civilization in India. There was the existence of chief cities like Harappa and Mohenjodaro, Vatsayana, Meghasthenese and Kautilya in their books mention the existence of cities during ancient times. The Muslim rulers built great cities like Agra and Delhi.

Then Britishers built many cities, but the exact origin of the city is last in the obscurity of the past. However, the first cities seem to have appeared in between 6000 and 5000 B.C. these cities were small and hard to distinguish from towns. But the city in its real sense came into existence by 3000 B.C. After that, there was a fall for more than 2000 years.

Then cities came into existence in Greece, Rome, India, Egypt etc. but in spite of the growth of cities, most of the population of India live in villages which is true even today. Though India has been a land of villages but has also had an urban tradition since time immemorial. Though. there were cities in ancient civilization as well as in Indian society, it is only in the last two centuries that urbanization has become a characteristic form of human life.

Causes of Urbanization :
Urbanization is a worldwide phenomenon. The percentage of urban population and growth of urban centres has increased rapidly At about 30 per cent of India’s total population lives in urban areas. Thus rapid growth of Urbanization is caused by several factors. Some of the factors which cause urbanization are as follows:

The national increase in population:
The population of the world increases naturally This provides employment to the increasing population and meets the increasing demand of products of this population. Industries are set up and urban centres grow revolving around these industries. Besides more and more people migrate from rural areas to urban areas.

In search of employment, better health facilities and better living a result of urbanization spreads. Besides now- a- days there is a growing trend to live in urban areas which resulted in the growth of new urban centres and the spread of urbanization.

Migration:
Migration is another important cause of urbanization. Migration means the movement of people from one place to another. It refers to a kind of geographical mobility. normally from rural areas to better opportunities. Sometimes urban people also migrate to rural areas to live in a natural and pollution-free environment. Migration helps in the spread of urbanization.

Expansion of urban areas:
The expansion of urban areas resulted in urbanization. Due to the expansion of urban areas the outlying rural areas become urban areas and the process of urbanization spreads over.

Industrialization:
Rapid industrialization is also another important cause of urbanization, Urban areas develop around industrial centres. Due to the installation of more industries, new urban centres grow which resulted in the spread of urbanization. Besides people migrate from villages to industrial towns to work there which helps in the spread of urbanization.

Impact or consequences of urbanization :
Urbanization is not an unmixed blessing. It has many negative impacts on human living and social relationships. It has resulted in the breakdown of traditional social institutions and brought a number of changes in society. However, some of the impacts or consequences of urbanization are discussed below.

Impact on family:
Urbanization has a number of impacts on families. It leads to a decline in family size. It leads to the breaking up of a joint family and the creation of a nuclear family. Similarly, it also affects family lies and led to the decline of family control. Urban family loses their control over children It also weakens family bonds.

Impact on marriage:
Urbanization greatly affects our marriage system. Parental control over marriages gradually declines. Marriage ceases to be religious and becomes secular. Rites and rituals in marriage decline day by day. Due to the free mixing of boys and girls the number of love marriages increases. It also affects mortal bonds and marriage ceases to be permanent. The number of divorces is increased. The age of marriage also increases, and many people even remain unmarried.

The decline in fellow and sympathy:
Urbanization leads to a decline in fellow feelings and sympathy. Due to rapid population growth and overcrowding nature, fellow feeling and sympathy sharply is declined among urban people. Urban people remain so busy that they have little time to take part in others’ jobs and sorrows. Even urban people do not know their next-door neighbours. Everyone is concerned only about himself and has little concern for others.

The decline in family control:
Urbanization leads to a decline in family control. In an urban area, we found a nuclear family and it has little control over its members Besides urban people have no time to spend with their family and to know what their children are doing. Loss of family ties resulted in the decline of family control.

The decline in the influence of Religion:
Religion has lost its control over the minds of urban people. Urban people are more materialistic in nature and is self- centred. Different religious rites, rituals and practices lose their importance in urban areas.

Impact on the role and status of women:
Urbanization considerably affects the role and status of women. It has led to the increasing role of women in different spehers of society. They are now enjoying economic freedom and are at par with their male counterpart. A large number of women are working in industries, offices and business houses. All this has led to a change in the status of women. The increasing role and status of women considerably affect family life and husband-wife relations.

Impact on caste :
Urbanization deeply affects our traditional caste system. Many caste rules are under change and the caste system has lost its earlier rigidities and become more flexible. People are no more following their caste occupations and not obeying caste rules even during marriage. More and more intercaste marriages are taking place and some caste associations are emerging caste is now playing a major role in politics.

Development of slums:
One of the important consequences of urbanization is the development of slums. Due to the rapid growth of population and shortage of land area in urban areas most of people are living in slums. Their slums are the breeding ground for criminal activities and the spread of diseases.

The decline in moral values:
Another evil impact of urbanization is the degeneration of the moral values of urban dwellers. Due to the spread of education, economic independence, the decline of religion, and the growth of materialism, there is a great deal of change in the moral values of people which causes many social problems.

Question 6.
Define globalization and discuss its aims and features?
Answer:
The term globalization comes from the word global means covering or relating to the whole world. In other words, global means looking at everything from the whole world’s point of view not an individual point of view. It means borderless development internationalization of all aspects of human life. It also means thinking, doing and producing globally. Globalization is mainly economic in character.

now- a – days globalization is active in the economic field means economic globalization. It refers process of increasing economic integration and growing economic interdependence among countries. Because of globalization whole world inter linked and inter-connected through economic social, political and cultural relations.

Globalization means manufacturing things or products in the most effective way anywhere in the world it aims at procuring raw materials and management personnel from anywhere in the world. Globalization considers the entire world as a market. Globalization also refers to the process of opening up national markets to the global market.

Definitions:
According to Anita, “Globalization is a process through which an increasingly free flow of ideas, people, goods and capital leads to the integration of economies and societies. According to D.N. Dhanagare “globalization refers to the growing economic integration international level based significantly or activities of multinational corporations”.

According to the European Commission, “ globalization is the process by which markets the productions in different countries are becoming increasingly interdependent dynamic of trade in goods and services and flows of capital technology”. Anthony Gidden, Globalization can be defined as the intensification of worldwide social relations, which link distant localities.

such a way that local happenings are shaped by events occurring many miles away and vice-versa”. According to MC Grew, “Globalization refers to those processes operating at a global scale which cut across national boundaries integrating of connecting communities and organizations in space-time combinations making the world in reality and in experience more interconnected” Aims of Globalization:

• Opening up national economics and developing a single economic system.
• Reduction of trade barriers and free movement of products.
• The disintegration of geographic boundaries.
• Free flow of international trade.
• Integration of local economy with the worked economy.

Features of Globalization:
Globalization has the following features.

A complex process:
Globalization is a complex process. Increasing interdependence among nations, free flow of products, labour and trade and increasing socio-cultural contacts among nations makes it more complex and complicated.

A composite process:
Globalization is a composite process. Because a combination of a series of developments in the world led to its emergence. Development, in science and technology, development in die field of communication, increased social mobility and a number of other developments led to the development of globalization. A single cause factor or development is not responsible for globalization. Hence, it is a composite process.

A historical process :
Globalization is a historical process because erosion of the process goes to the period of the industrial revolution of the 16th century, but the trend for business transcending national boundaries is very old Hence, globalization is not a new concept but rather very ancient in nature.

An integrating process:
Globalization is a process of increasing economic integration. In this process markets, finance and technology are well integrated.

A multi-dimensional process:
Globalization is a multi-dimensional process because it has many faces. It can be understood from different angles. From an economic angle, it refers to the integration of the national economy with the world economy.

From a political angle, globalization refers to the emergence of a world state with the erosion of the sovereignty of the state. From a cultural angle, it refers to increased socio-cultural contact among nations all over the world. From an ideological angle, it refers to the victory of liberalization and capitalism over socialism. Globalization is associated with new technology like computers, the internet, electronic media, television and many others.

Globalization envisions the development of the world community. Globalization is also characterized by the development of multinational business corporations. Globalization is a self-contradictory process as. it contains the existence of contradictory forces like integration versus fragmentation, universalization versus particularization, and homogeneity versus heterogeneity.

Globalization is a dynamic process The process of globalization started in India in 1990. India opened its economy to the world economy then, but in the beginning, it follows a protective policy to safeguard its own industries. But now things have changed.

Question 7.
What is industrialization changing life and its positive effects on the Industrial Revolution?
Answer:
The Industrial Revolution affected every part of life in Great Britain but proved to be a mixed blessing. Eventually, industrialization led to a better quality of life for most people. the change in machine production initially caused human suffering Rapid industrialization brought plentiful Jobs but out also caused unhealthy working conditions air and water pollution and the illness of child labour.

It also led to rising class tensions, especially between the working class and the middle class. The pace of industrialization accelerated rapidly in Britain. By the 1800 people could earn higher wages in factors than a form. With this money, more people could offer to heat their homes with coal from walls and dine on Scottish beef. They were better clothing too, woven on power looms on England’s Industrial cities swelled with waves of job seekers.

Positive Effects of the Industrial Revolution Despite the problems followed industrialization the industrial Revolution had a number of positive effects. It created jobs for workers. It contributed to the wealth of the nation. It fastened technological progress and invention. It greatly increased the production of goods and raised the standard of living, perhaps.

most important it provided the hope of improvement in people’s lives. industrial Revolution produced a number of other benefits as well. These included healthier diets, better housing the cheaper, mass-produced clothing. Because the Industrial Revolution created a demand for engineers as well as clerical and professional workers, it expanded educational opportunities.

The middle and upper classes prospered immediately from the Industrial Revolution for the workers it took longer but their lives gradually improved during the 1800s Labourers eventually won higher wages shorter horns, and better working conditions after they joined together to form labour unions. The long-term effects of the Industrial Revolution are still evident most people today in industrialized countries can be offered consumer goods that would have been considered luxuries 60 or 60 years ago.

In addition, their living and working conditions are much improved over those of workers in the 19th century. Also, profits derived from industrialization produced tax revenues. These funds have allowed local state and federal governments to invest in urban improvements and the standard of living of most city dwellers.

Question 8.
Defining Modernization and politicians’ modernization?
Answer:
Modernization originally referred to the contrast and transition between a traditional agrarian society and the kind of modem society that is based on trade and industry, For example, traditional and modern would describe the difference between medieval England and late-Victorian Britain. A traditional society is vertically organized by hierarchical division by class or caste – a specialization of prestige.

But a modem society is horizontally organized by function, and the major social systems include the political system public administration (social service) the armed forces the legal system the economy religion, education the health service and the mass media. while a traditional society is like a pyramid of top-down authority a modem society is more like a mosaic held together the cement of mutual interdependence.

A further contrast is that traditional societies consist of a single, unified system with a single centre of power, while a modem society is composed of a plurality of autonomous systems each other do not absorb each other. Modem societies are fundamentally hetero- generous with multiple centres of power and thus is no accident but intrinsic to their nature.

Indeed the continued process of modernization tends to break down any remaining vestiges of hierarchy and centralized domination of social functions. Modernization is a product of the selection process. This means that not all political initiatives that are self-described as modernization can be considered genuine modernization.

Many such modernizing reforms actually diminish the selection processes that tend to be generally complex functionally. Thus mismatch between theoric and reality arises from a terminological ambiguity which modernization means different things different contexts. In this book, we follow humans in arguing that true modernization is the increase in the functional specialization of societies.

that the functionality of a social system is defined by its having prevailed over other social system variants during a historical competition. In other words, functionality is relative and the most functional system is one that has displaced other system variants a competitive, Selection processes are therefore intrinsic to modernization.

But another use of modernization is as a synonym for rationalization. Rationalization usually entails the reform of a social system by central government along the lines of making out more of a rational bureaucracy involving standardization of exploit procedures hierarchical command system The confusion is across from the fact that (as weber famously noted).

the emergence of rational bureaucracies characterized many modem states such as the nineteenth century. Germany later thus ideal of rational bureaucracy as being the most efficient mode of the organization was to dominate the social system of the USSR and outs satellites.

Modernisation and Its Impact on Indian society:
The term’Modemisation’ is a broader and more complex term. According to S.H. Alatas, “Modernisation is a process by which modem scientific knowledge is introduced in the society with the ultimate purpose of achieving a better and more satisfactory life in the broadest sense of the term accepted by the society concerned”.

Prof Yogendra Singh says, “Modernisation symbolizes a rational attitude towards issues and their evaluation but not from a particularistic point of view. He also says modernization is rooted in scientific knowledge, technological skill. Prof S.Ci Dube says “Modernisation refers to a common behavioural pattern characterised by A rational and scientific worldview.

Growth and ever-increasing application of science and technology. Adaptation of new institutions emerged in society to cope with the new situation dominated by science and technology. C.E. Black in his writing, “Dynamics Modernisation” modernisation as “Modernisation is a process by which historically evolved institutions are adopted.

the rapidly changing functions that reflect the unprecedented increase in man’s knowledge permitting control over environment, accompany the scientific revolution”. Here, Black has given prime importance to the institutions and their roles the process of modernisation. W.E. Moore (1961) suggested that a modem society has specific economic, political and cultural characteristics.

In the economic sphere, modern society is characterised by:
Development in technology. Specialization the economic role. Scope for saving and investment. Expansion of market(from local international).

In the political sphere modernization of society expects:
Declining of traditional rulers. Formulation of ideology for the rulers to handle the power. Decentralization of power among the members of the society. The scope must be provided to all to participate in the decision-making process.

In the cultural sphere, a modernizing society is characterised by:
Growing differential among major elements of culture like religion, philosophy and science. Spread of literacy, secular education. Introduction of a complex institutional system for the advancement of specialized roles. Expansion of media communication.

Development of new cultural elements based on:
Progress and improvement Expression of ability Emphasis on the dignity of the individual and his efficiency, Modernisation is a process of adaptation of new values, cultural elements and technology in the various fields of life. It is indeed the ability of a society of confronting, overcome and prepare itself to meet new challenges.

While doing so society adopts two methods:
By rearranging its social structure. By modifying the traditional norms and values. The learner emphasized mobility high-level participation. A modem man is more mobile in the sense that he can more frequently move from one place to another and from one occupational another, from one status to another. A high degree of participation indicates a strong sense of participation in common affairs of the state and community.

Characteristics of Modernisation:

• It is a revolutionary process.
• It is a multidimensional process.
• It is a universal process.
• It is a complex process.
• It is a global process.
• It is an irreversible process.
• It is a continuous and lengthy process.
• It is a systematic process
• It indicates scientific temper, rationality and secular attitude.
• It is a phased process.
• Modernized society is an open society
• It is a progressive society.
• It is a critical process because it requires not only a relatively stable new structure but is also capable of adopting continuously changing conditions and problems.
• It is a centralized process.

Eisenstadt (1965) in his article, Transformation of Social, Political and Cultural Orders in Modernisation” has given his opinion modernisation requires three structural characteristics of a society. Firstly, a high level of structural differentiation. Secondly, high level of social mobilization and thirdly relatively centralized and autonomous institutional frameworks.

Modernisation is critical in the sense that it requires not only a relatively stable new structure in society but also expects that the society acquires the capability to adapt to continuously changing conditions and problems. Its success depends on the ability of society to respond to the elements. But all societies don’t respond to modernisation uniformly.

Herbert Blunter in his writing. Industrialisation and the Traditional Order” has mentioned five different ways through which a traditional society can respond to the process of modernisation.

Rejective response:
A traditional society may not like the elements of modernisation and the society may reject it. Mainly two factors come to the forefront to reject modernization. Human factors included powerful groups, zamindars/ landlords, middlemen etc. protect their vested interests. Values system of the society which includes traditional values, customs, belief systems etc. Both factors try to maintain traditional order and reject the process of modernisation.

Disjunctive Response:
In this type of response, modernisation as a process operates as a detached development. The old elements and new elements co-exist but without any interference. People do not face any type of conflicting situation due to modernisation. They could lead their traditional life.

Assimilative Response:
Society, in this case, accepts elements of modernisation without affecting it. organisation and way of life. It assimilates the elements within its system without disruption. For example, in Indian rural society, the farmers use fertilizer and other modem machinery like tractors without affecting their pattern of life.

Supportive Response :
In a supportive response, society accepts modem elements to strengthen the conditional order. Traditional groups and institutions want to take advantage of the use of modem elements. Here modernisation acts as the supportive source of the traditional pattern. For example, the introduction of science and technology in the educational system.

Disruptive Response:
This type of response takes place when the traditional order is underestimated at many points. It occurs when society tries to accommodate modem elements in the traditional order. For example, the situation of the Odia language in Odia. Considering these five responses two types of situations may occur in society.

In one situation society may respond to all these at different points or periods and in another situation, society may express all these responses with different combinations. In India, response to modernisation depends on three factors as it constitutes a multi-dimensional process. Firstly, the nature of the choice that our society has made on the preference of the people in accepting modem elements.

Secondly, the interest of the people in using modem elements also counts much for that expresses the nature of our response to the changes due to modernisation. Thirdly, the role of the cultural tradition based on history is important as a value system controls our behaviour in using and interpreting modem elements.

Modernsation in India:
Due to modernisation, so many changes are founded in India:

• Introduction of new institutions like banking, mass media communication etc.
• Introduction of new value systems such as equality, justice, individualism, secularism etc.
• Acceptance of scientific innovation.
• Increase in the standard of living.
• Introduction of large-scale industries.
• Restructuring of the political system, i.e. introduction of democracy.
• Introduction of structural changes in social institutions like marriage, family, caste, etc.
• The emergence of the middle class.
• There are some eliminative changes like the disappearance of cultural traits, behaviour patterns, values etc. For example, the abolition of feudal power.
• There is shifting of attitude from sacred to secular.
• The emergence of new forms is because of the synthesis of old and new elements. For example,- the nuclear family in structured but functioning as a joint.
• Adoption of new cultural traits as a new election system.

Question 9.
What is Industrialization? Discuss its Impact?
Answer:
Industrialization is the process by which an economy is transformed from primarily agricultural to one based on the manufacturing of goods. Individual manual labour as often. replaced by mechanized mass production and craftsmen are replaced by assembly lines characteristic of industrialization include economic growth, more efficient division of labour and the use of technological innovation to solve problems as opposed to dependency on conditions outside human control.

Industrialization is most commonly associated with the European Industrial Revolution of the 18th and early centuries. The inset of the second world war also led to a great deal of industrialization which resulted in the growth and development of large urban centres and submits outs effects on society are still undetermined to some extent, however, it has resulted in a lower birthrate and a higher average income.

Impact on Indian Society: The Industrial Revolution traces its roots to the late 19th century in Britain. The growth of the metals and textiles industries allowed for the mass production of basic personal and commercial goods. As manufacturing activities grew transportation, finance and communications industries expanded to support the new production capacities.

The Industrial Revolution led to improved ented expansion in wealth and financial well-being for some. It also led to increased labour specialization and allowed cities to support a larger population motivating a rapid demographic shift, people left rural areas in large numbers seeking potential fortunes in budding industries.

The revolution quickly spread beyond Britain with manufacturing centres being established in continental Europe and the United States. World War II created unprecedented demand for certain manufactured goods, leading to the building of production capacity. After the war reconstruction in Europe occurred alongside a massive population expansion in North America.

There provided further catalysts that kept capacity utilization high and stimulated future growth of industrial activity. Innovation specialization and wealth creations were the causes and effects of industrialization in this period. The late 20th century was noteworthy for rigid industrialization in other parts of the worked notably East Asia. The Asian Tigers of their own industrial revolution after moving towards a merely mixed economy and away from heavy central planning.